chapter 4 resource masters - commack schools 4...4 pdf pass chapter 4 1 glencoe algebra 1...
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Chapter 4 Resource Masters
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Copyright © by The McGraw-Hill Companies, Inc.
All rights reserved. The contents, or parts thereof, may be reproduced in print form for non-profit educational use with Glencoe Algebra 1, provided such reproductions bear copyright notice, but may not be reproduced in any form for any other purpose without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, network storage or transmission, or broadcast for distance learning.
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ISBN: 978-0-07-660499-9MHID: 0-07-660499-3
Printed in the United States of America.
1 2 3 4 5 6 7 8 9 DOH 16 15 14 13 12 11
CONSUMABLE WORKBOOKS Many of the worksheets contained in the Chapter Resource Masters booklets are available as consumable workbooks in both English and Spanish.
MHID ISBNStudy Guide and Intervention Workbook 0-07-660292-3 978-0-07-660292-6Homework Practice Workbook 0-07-660291-5 978-0-07-660291-9
Spanish VersionHomework Practice Workbook 0-07-660294-X 978-0-07-660294-0
Answers For Workbooks The answers for Chapter 4 of these workbooks can be found in the back of this Chapter Resource Masters booklet.
ConnectED All of the materials found in this booklet are included for viewing, printing, and editing at connected.mcgraw-hill.com.
Spanish Assessment Masters (MHID: 0-07-660289-3, ISBN: 978-0-07-660289-6) These masters contain a Spanish version of Chapter 4 Test Form 2A and Form 2C.
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Teacher’s Guide to Using the Chapter 4 Resource Masters ..............................................iv
Chapter Resources Chapter 4 Student-Built Glossary ...................... 1Chapter 4 Anticipation Guide (English) ............. 3Chapter 4 Anticipation Guide (Spanish) ............ 4
Lesson 4-1Graphing Equations in Slope-Intercept Form Study Guide and Intervention ............................ 5Skills Practice .................................................... 7Practice ............................................................. 8Word Problem Practice ...................................... 9Enrichment ...................................................... 10
Lesson 4-2Writing Equations in Slope-Intercept Form Study Guide and Intervention ...........................11Skills Practice .................................................. 13Practice ........................................................... 14Word Problem Practice .................................... 15Enrichment ...................................................... 16
Lesson 4-3Writing Equations in Point-Slope FormStudy Guide and Intervention .......................... 17Skills Practice .................................................. 19Practice ........................................................... 20Word Problem Practice .................................... 21Enrichment ...................................................... 22Graphing Calculator Activity ............................ 23
Lesson 4-4Parallel and Perpendicular Lines Study Guide and Intervention .......................... 24Skills Practice .................................................. 26Practice ........................................................... 27Word Problem Practice .................................... 28Enrichment ...................................................... 29
Lesson 4-5Scatter Plots and Lines of Fit Study Guide and Intervention .......................... 30Skills Practice .................................................. 32Practice ........................................................... 33Word Problem Practice .................................... 34Enrichment ...................................................... 35Spreadsheet Activity ........................................ 36
Lesson 4-6Regression and Median-Fit Lines Study Guide and Intervention .......................... 37Skills Practice .................................................. 39Practice ........................................................... 40Word Problem Practice .................................... 41Enrichment ...................................................... 42
Lesson 4-7Inverse Linear FunctionsStudy Guide and Intervention .......................... 43Skills Practice .................................................. 45Practice ........................................................... 46Word Problem Practice .................................... 47Enrichment ...................................................... 48
AssessmentStudent Recording Sheet ................................ 49Rubric for Scoring Extended Response .......... 50Chapter 4 Quizzes 1 and 2 ............................. 51Chapter 4 Quizzes 3 and 4 ............................. 52Chapter 4 Mid-Chapter Test ............................ 53Chapter 4 Vocabulary Test ............................... 54Chapter 4 Test, Form 1 .................................... 55Chapter 4 Test, Form 2A ................................. 57
Chapter 4 Test, Form 2B ................................. 59Chapter 4 Test Form 2C .................................. 61Chapter 4 Test Form 2D .................................. 63Chapter 4 Test Form 3 ..................................... 65Chapter 4 Extended-Response Test ................ 67Standardized Test Practice .............................. 68
Answers ........................................... A1–A34
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Teacher’s Guide to Using the Chapter 4 Resource Masters
The Chapter 4 Resource Masters includes the core materials needed for Chapter 4. These materials include worksheets, extensions, and assessment options. The answers for these pages appear at the back of this booklet.
All of the materials found in this booklet are included for viewing, printing, and editing at connectED.mcgraw-hill.com.
Chapter Resources
Student-Built Glossary (pages 1–2) These masters are a student study tool that presents up to twenty of the key vocabulary terms from the chapter. Students are to record definitions and/or examples for each term. You may suggest that students highlight or star the terms with which they are not familiar. Give this to students before beginning Lesson 4-1. Encourage them to add these pages to their mathematics study notebooks. Remind them to complete the appropriate words as they study each lesson.
Anticipation Guide (pages 3–4) This master, presented in both English and Spanish, is a survey used before beginning the chapter to pinpoint what students may or may not know about the concepts in the chapter. Students will revisit this survey after they complete the chapter to see if their perceptions have changed.
Lesson ResourcesStudy Guide and Intervention These masters provide vocabulary, key concepts, additional worked-out examples and Check Your Progress exercises to use as a reteaching activity. It can also be used in conjunction with the Student Edition as an instructional tool for students who have been absent.
Skills Practice This master focuses more on the computational nature of the lesson. Use as an additional practice option or as homework for second-day teaching of the lesson.
Practice This master closely follows the types of problems found in the Exercises section of the Student Edition and includes word problems. Use as an additional practice option or as homework for second-day teaching of the lesson.
Word Problem Practice This master includes additional practice in solving word problems that apply the concepts of the lesson. Use as an additional practice or as homework for second-day teaching of the lesson.
Enrichment These activities may extend the concepts of the lesson, offer an historical or multicultural look at the concepts, or widen students’ perspectives on the mathematics they are learning. They are written for use with all levels of students.
Graphing Calculator, TI-Nspire, or Spreadsheet Activities These activities present ways in which technology can be used with the concepts in some lessons of this chapter. Use as an alternative approach to some concepts or as an integral part of your lesson presentation.
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Assessment OptionsThe assessment masters in the Chapter 4 Resource Masters offer a wide range of assessment tools for formative (monitoring) assessment and summative (final) assessment.
Student Recording Sheet This master corresponds with the standardized test practice at the end of the chapter.
Extended Response Rubric This master provides information for teachers and stu-dents on how to assess performance on open-ended questions.
Quizzes Four free-response quizzes offer assessment at appropriate intervals in the chapter.
Mid-Chapter Test This 1-page test provides an option to assess the first half of the chapter. It parallels the timing of the Mid-Chapter Quiz in the Student Edition and includes both multiple-choice and free-response questions.
Vocabulary Test This test is suitable for all students. It includes a list of vocabulary words and 11 questions to assess students’ knowledge of those words. This can also be used in conjunction with one of the leveled chapter tests.
Leveled Chapter Tests
• Form 1 contains multiple-choice ques-tions and is intended for use with below grade level students.
• Forms 2A and 2B contain multiple-choice questions aimed at on grade level students. These tests are similar in format to offer comparable testing situations.
• Forms 2C and 2D contain free-response questions aimed at on grade level students. These tests are similar in format to offer comparable testing situations.
• Form 3 is a free-response test for use with above grade level students.
All of the above mentioned tests include a free-response Bonus question.
Extended-Response Test Performance assessment tasks are suitable for all students. Sample answers and a scoring rubric are included for evaluation.
Standardized Test Practice These three pages are cumulative in nature. It includes three parts: multiple-choice questions with bubble-in answer format, griddable questions with answer grids, and short-answer free-response questions.
Answers• The answers for the Anticipation Guide
and Lesson Resources are provided as reduced pages.
• Full-size answer keys are provided for the assessment masters.
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Chapter 4 1 Glencoe Algebra 1
Student-Built Glossary
This is an alphabetical list of the key vocabulary terms you will learn in Chapter 4. As you study the chapter, complete each term’s definition or description. Remember to add the page number where you found the term. Add these pages to your Algebra Study Notebook to review vocabulary at the end of the chapter.
Vocabulary TermFound
on PageDefi nition/Description/Example
best-fit line
bivariate data
correlation coefficientkawr·uh·LAY·shun
inverse function
inverse relation
line of fit
linear extrapolationihk·STRA·puh·LAY·shun
linear interpolationihn·TUHR·puh·LAY·shun
(continued on the next page)
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Chapter 4 2 Glencoe Algebra 1
Student-Built Glossary (continued)
Vocabulary TermFound
on PageDefi nition/Description/Example
linear regression
median-fit line
parallel lines
perpendicular linesPUHR·puhn·DIH·kyuh·luhr
residual
scatter plot
slope-intercept formIHN·tuhr·SEHPT
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Chapter 4 3 Glencoe Algebra 1
Anticipation GuideEquations of Linear Functions
Before you begin Chapter 4
• Read each statement.
• Decide whether you Agree (A) or Disagree (D) with the statement.
• Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (Not Sure).
After you complete Chapter 4
• Reread each statement and complete the last column by entering an A or a D.
• Did any of your opinions about the statements change from the first column?
• For those statements that you mark with a D, use a piece of paper to write an example of why you disagree.
STEP 1A, D, or NS
StatementSTEP 2A or D
1. The slope of a line given by an equation in the form y = mx + b can be determined by looking at the equation.
2. The y-intercept of y = 12x - 8 is 8. 3. If two points on a line are known, then an equation can be
written for that line. 4. An equation in the form y = mx + b is in point-slope form. 5. If a pair of lines are parallel, then they have the same slope. 6. Lines that intersect at right angles are called perpendicular
lines. 7. A scatter plot is said to have a negative correlation when the
points are random and show no relationship between x and y.
8. The closer the correlation coefficient is to zero, the more closely a best-fit line models a set of data.
9. The equations of a regression line and a median-fit line are very similar.
10. An inverse relation is obtained by exchanging the x-coordinates with the y-coordinates of each ordered pair of the original relation.
Step 1
Step 2
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PDF 2nd
Capítulo 4 4 Álgebra 1 de Glencoe
4 Ejercicios preparatoriosEcuaciones de Funciones Lineales
Antes de comenzar el Capítulo 4
• Lee cada enunciado.
• Decide si estás de acuerdo (A) o en desacuerdo (D) con el enunciado.
• Escribe A o D en la primera columna O si no estás seguro(a) de la respuesta, escribe NS (No estoy seguro(a)).
Después de completar el Capítulo 4
• Vuelve a leer cada enunciado y completa la última columna con una A o una D.
• ¿Cambió cualquiera de tus opiniones sobre los enunciados de la primera columna?
• En una hoja de papel aparte, escribe un ejemplo de por qué estás en desacuerdo con los enunciados que marcaste con una D.
PASO 1A, D, o NS
EnunciadoPASO 2A o D
1. La pendiente de una recta dada por una ecuación de la forma y = mx + b se puede determinar mediante la observación de la ecuación.
2. La intersección y de y = 12x - 8 es 8. 3. Si se conocen dos puntos sobre una recta, entonces se puede
escribir una ecuación para esa recta. 4. Una ecuación de la forma y = mx + b está en forma
punto-pendiente.
6. A las rectas que se intersecan en ángulos rectos se lesllama rectas perpendiculares.
7. Se dice que un diagrama de dispersión tiene correlación negativa cuando los puntos son aleatorios y no muestran relación entre x y y.
8. Entre más cercano se encuentre de cero el coeficiente de correlación, mejor modela un conjunto de datos la recta de mejor ajuste.
9. La ecuación de una línea de regresión y una recta de mediano ajuste son muy parecidas.
10. Una relación inversa es obtenida cambiando las x-coordenadas con las y-coordenadas de cada par pedido de la relación original.
Paso 1
Paso 2
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Chapter 4 5 Glencoe Algebra 1
Study Guide and InterventionGraphing Equations in Slope-Intercept Form
Slope-Intercept FormSlope-Intercept Form y = mx + b, where m is the slope and b is the y-intercept
Write an equation in slope-intercept form for the line with a slope of -4 and a y-intercept of 3.
y = mx + b Slope-intercept form
y = -4x + 3 Replace m with -4 and b with 3.
Graph 3x - 4y = 8.
3x - 4y = 8 Original equation
-4y = -3x + 8 Subtract 3x from each side.
-4y
−
-4 = -3x + 8 −
-4 Divide each side by -4.
y = 3 −
4 x - 2 Simplify.
The y-intercept of y = 3 −
4 x - 2 is -2 and the slope is 3 −
4 . So graph the point (0, -2). From
this point, move up 3 units and right 4 units. Draw a line passing through both points.
ExercisesWrite an equation of a line in slope-intercept form with the given slope and y-intercept.
1. slope: 8, y-intercept -3 2. slope: -2, y-intercept -1 3. slope: -1, y-intercept -7
Write an equation in slope-intercept form for each graph shown.
4.
(0, –2)
(1, 0) x
y
O
5.
(3, 0)
(0, 3)
x
y
O
6.
(4, –2)
(0, –5)
xy
O
Graph each equation.
7. y = 2x + 1 8. y = -3x + 2 9. y = -x - 1
x
y
O
x
y
O
x
y
O
(0, –2)
(4, 1)
x
y
O
3x - 4y = 8
Example 1
Example 2
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Chapter 4 6 Glencoe Algebra 1
Study Guide and Intervention (continued)
Graphing Equations in Slope-Intercept Form
Modeling Real-World Data
MEDIA Since 1999, the number of music cassettes sold has decreased by an average rate of 27 million per year. There were 124 million music cassettes sold in 1999.
a. Write a linear equation to find the average number of music cassettes sold in any year after 1999.
The rate of change is -27 million per year. In the first year, the number of music cassettes sold was 124 million. Let N = the number of millions of music cassettes sold. Let x = the number of years since 1999. An equation is N = -27x + 124.
b. Graph the equation. The graph of N = -27x + 124 is a line that passes
through the point at (0, 124) and has a slope of -27.
c. Find the approximate number of music cassettes sold in 2003.
N = -27x + 124 Original equation
N = -27(4) + 124 Replace x with 4.
N = 16 Simplify.
There were about 16 million music cassettes sold in 2003.
Exercises 1. MUSIC In 2001, full-length cassettes represented 3.4% of
total music sales. Between 2001 and 2006, the percent decreased by about 0.5% per year.a. Write an equation to find the percent P of recorded music
sold as full-length cassettes for any year x between 2001 and 2006.
b. Graph the equation on the grid at the right.c. Find the percent of recorded music sold
as full-length cassettes in 2004.
2. POPULATION The population of the United States is projected to be 300 million by the year 2010. Between 2010 and 2050, the population is expected to increase by about 2.5 million per year.a. Write an equation to find the population P in any year x
between 2010 and 2050. b. Graph the equation on the grid at the right.
c. Find the population in 2050.
Full-length Cassette Sales
Perc
ent o
f Tot
al M
usic
Sal
es
1.5%
2.0%
1.0%
2.5%
3.0%
3.5%
Years Since 20013210 54
Projected UnitedStates Population
Years Since 2010
Popu
latio
n (m
illio
ns)
0 20 40 x
P
400
380
360
340
320
300
Music Cassettes Sold
Cass
ette
s (m
illio
ns)
50
75
25
0
100
125
Years Since 1999321 5 74 6
Example
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Chapter 4 7 Glencoe Algebra 1
Skills PracticeGraphing Equations in Slope-Intercept Form
Write an equation of a line in slope-intercept form with the given slope and y-intercept.
1. slope: 5, y-intercept: -3 2. slope: -2, y-intercept: 7
3. slope: -6, y-intercept: -2 4. slope: 7, y-intercept: 1
5. slope: 3, y-intercept: 2 6. slope: -4, y-intercept: -9
7. slope: 1, y-intercept: -12 8. slope: 0, y-intercept: 8
Write an equation in slope-intercept form for each graph shown.
9.
(2, 1)
(0, –3)
x
y
O
10.
(0, 2)
(2, –4)
x
y
O
11.
(0, –1)(2, –3)
x
y
O
Graph each equation. 12. y = x + 4 13. y = -2x - 1 14. x + y = -3
x
y
O
x
y
O
x
y
O
15. VIDEO RENTALS A video store charges $10 for a rental card plus $2 per rental.
a. Write an equation in slope-intercept form for the total cost c of buying a rental card and renting m movies.
b. Graph the equation.
c. Find the cost of buying a rental card and renting 6 movies.
Video StoreRental Costs
Tota
l Cos
t ($)
10
0
12
14
16
18
20
c
Movies Rented1 2 3 4 5 m
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Chapter 4 8 Glencoe Algebra 1
PracticeGraphing Equations in Slope-Intercept Form
Write an equation of a line in slope-intercept form with the given slope and y-intercept.
1. slope: 1 −
4 , y-intercept: 3 2. slope: 3 −
2 , y-intercept: -4
3. slope: 1.5, y-intercept: -1 4. slope: -2.5, y-intercept: 3.5
Write an equation in slope-intercept form for each graph shown.
5.
(–5, 0)
(0, 2)
x
y
O
6.
(–2, 0)
(0, 3)
x
y
O
7.
(–3, 0)
(0, –2)
x
y
O
Graph each equation.
8. y = -
1 −
2 x + 2 9. 3y = 2x - 6 10. 6x + 3y = 6
x
y
O
x
y
O
x
y
O
11. WRITING Carla has already written 10 pages of a novel. She plans to write 15 additional pages per month until she is finished.
a. Write an equation to find the total number of pages P written after any number of months m.
b. Graph the equation on the grid at the right.
c. Find the total number of pages written after 5 months.
Carla’s Novel
Months
Page
s W
ritte
n
20 4 61 3 5 m
P
100
80
60
40
20
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Chapter 4 9 Glencoe Algebra 1
Word Problem PracticeGraphing Equations in Slope-Intercept Form
1. SAVINGS Wade’s grandmother gave him $100 for his birthday. Wade wants to save his money to buy a new MP3 player that costs $275. Each month, he adds $25 to his MP3 savings. Write an equation in slope-intercept form for x, the number of months that it will take Wade to save $275.
2. CAR CARE Suppose regular gasoline costs $2.76 per gallon. You can purchase a car wash at the gas station for $3. The graph of the equation for the cost of x gallons of gasoline and a car wash is shown below. Write the equation in slope-intercept form for the line.
Gasoline (gal)3210 54 987 10
y
x6
Co
st o
f g
as a
nd
car
was
h (
$)
6
8
4
2
10
16
14
12
18
24
22
20
(4, 14.04)
(2, 8.52)
(0, 3)
3. ADULT EDUCATION Angie’s mother wants to take some adult education classes at the local high school. She has to pay a one-time enrollment fee of $25 to join the adult education community, and then $45 for each class she wants to take. The equation y = 45x + 25 expresses the cost of taking x classes. What are the slope and y-intercept of the equation?
4. BUSINESS A construction crew needs to rent a trench digger for up to a week. An equipment rental company charges $40 per day plus a $20 non-refundable insurance cost to rent a trench digger. Write and graph an equation to find the total cost to rent the trench digger for d days.
Days3210 54 9876
Pric
e ($
)
100
140
60
20
180
300
340
260
220
5. ENERGY From 2002 to 2005, U.S. consumption of renewable energy increased an average of 0.17 quadrillion BTUs per year. About 6.07 quadrillion BTUs of renewable power were produced in the year 2002.
a. Write an equation in slope-intercept form to find the amount of renewable power P (quadrillion BTUs) produced in year y between 2002 and 2005.
b. Approximately how much renewable power was produced in 2005?
c. If the same trend continues from 2006 to 2010, how much renewable power will be produced in the year 2010?
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Chapter 4 10 Glencoe Algebra 1
Enrichment
Using Equations: Ideal WeightYou can find your ideal weight as follows.A woman should weigh 100 pounds for the first 5 feet of height and 5 additional pounds for each inch over 5 feet (5 feet = 60 inches). A man should weigh 106 pounds for the first 5 feet of height and 6 additional pounds for each inch over 5 feet. These formulas apply to people with normal bone structures.To determine your bone structure, wrap your thumb and index finger around the wrist of your other hand. If the thumb and finger just touch, you have normal bone structure. If they overlap, you are small-boned. If they don’t overlap, you are large-boned. Small-boned people should decrease their calculated ideal weight by 10%. Large-boned people should increase the value by 10%.
Calculate the ideal weights of these people.1. woman, 5 ft 4 in., normal-boned 2. man, 5 ft 11 in., large-boned
3. man, 6 ft 5 in., small-boned 4. you, if you are at least 5 ft tall
For Exercises 5–9, use the following information.
Suppose a normal-boned man is x inches tall. If he is at least 5 feet tall, then x - 60 represents the number of inches this man is over 5 feet tall. For each of these inches, his ideal weight is increased by 6 pounds. Thus, his proper weight y is given by the formula y = 6(x - 60) + 106 or y = 6x - 254. If the man is large-boned, the formula becomes y = 6x - 254 + 0.10(6x - 254).
5. Write the formula for the weight of a large-boned man in slope-intercept form.
6. Derive the formula for the ideal weight y of a normal-boned female with height x inches. Write the formula in slope-intercept form.
7. Derive the formula in slope-intercept form for the ideal weight y of a large-boned female with height x inches.
8. Derive the formula in slope-intercept form for the ideal weight y of a small-boned male with height x inches.
9. Find the heights at which the ideal weights of normal-boned malesand large-boned females would be the same.
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Chapter 4 11 Glencoe Algebra 1
ExercisesWrite an equation of the line that passes through the given point and has the given slope.
1. (3, 5)
x
y
O
m = 2
2.
(0, 0)x
y
O
m = –2
3.
(2, 4)
x
y
O
m = 12
4. (8, 2); slope -
3 −
4 5. (-1, -3); slope 5 6. (4, -5); slope -
1 −
2
7. (-5, 4); slope 0 8. (2, 2); slope 1 −
2 9. (1, -4); slope -6
10. (-3, 0), m = 2 11. (0, 4), m = -3 12. (0, 350), m = 1 −
5
Study Guide and InterventionWriting Equations in Slope-Intercept Form
Write an Equation Given the Slope and a Point
Write an equation ofthe line that passes through (-4, 2) with a slope of 3.The line has slope 3. To find the y-intercept, replace m with 3 and (x, y) with (-4, 2) in the slope-intercept form. Then solve for b. y = mx + b Slope-intercept form
2 = 3(-4) + b m = 3, y = 2, and x = -4
2 = -12 + b Multiply.
14 = b Add 12 to each side.
Therefore, the equation is y = 3x + 14.
Write an equation of the linethat passes through (-2, -1) with a slope of 1 −
4 .
The line has slope 1 −
4 . Replace m with 1 −
4 and (x, y)
with (-2, -1) in the slope-intercept form. y = mx + b Slope-intercept form
-1 = 1 −
4 (-2) + b m = 1
−
4 , y = -1, and x = -2
-1 = - 1 −
2 + b Multiply.
- 1 −
2 = b Add
1
−
2 to each side.
Therefore, the equation is y = 1 −
4 x - 1 −
2 .
Example 1 Example 2
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Chapter 4 12 Glencoe Algebra 1
Study Guide and Intervention (continued)
Writing Equations in Slope-Intercept Form
Write an Equation Given Two Points
Write an equation of the line that passes through (1, 2) and (3, -2). Find the slope m. To find the y-intercept, replace m with its computed value and (x, y) with (1, 2) in the slope-intercept form. Then solve for b.
m = y 2 - y 1 − x 2 - x 1
Slope formula
m = -2 - 2 −
3 - 1 y
2 = -2, y
1 = 2, x
2 = 3, x
1 = 1
m = -2 Simplify.
y = mx + b Slope-intercept form
2 = -2(1) + b Replace m with -2, y with 2, and x with 1.
2 = -2 + b Multiply.
4 = b Add 2 to each side.
Therefore, the equation is y = -2x + 4.
ExercisesWrite an equation of the line that passes through each pair of points.
1. (1, 1)
(0, –3)
x
y
O
2. (0, 4)
(4, 0) x
y
O
3.
(0, 1)
(–3, 0) x
y
O
4. (-1, 6), (7, -10) 5. (0, 2), (1, 7) 6. (6, -25), (-1, 3)
7. (-2, -1), (2, 11) 8. (10, -1), (4, 2) 9. (-14, -2), (7, 7)
10. (4, 0), (0, 2) 11. (-3, 0), (0, 5) 12. (0, 16), (-10, 0)
Example
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Chapter 4 13 Glencoe Algebra 1
Write an equation of the line that passes through the given point with the given slope.
1.
(–1, 4)
x
y
O
m = –3
2. (4, 1)
x
y
O
m = 1
3.
(-1, 2)
x
y
O
m = 2
4. (1, 9); slope 4 5. (4, 2); slope -2 6. (2, -2); slope 3
7. (3, 0); slope 5 8. (-3, -2); slope 2 9. (-5, 4); slope -4
Write an equation of the line that passes through each pair of points.
10. (–2, 3)
(3, –2)
x
y
O
11.
(–1, –3)
(1, 1)x
y
O
12.
(2, –1)
(0, 3)
x
y
O
13. (1, 3), (-3, -5) 14. (1, 4), (6, -1) 15. (1, -1), (3, 5)
16. (-2, 4), (0, 6) 17. (3, 3), (1, -3) 18. (-1, 6), (3, -2)
19. INVESTING The price of a share of stock in XYZ Corporation was $74 two weeks ago. Seven weeks ago, the price was $59 a share.
a. Write a linear equation to find the price p of a share of XYZ Corporation stock w weeks from now.
b. Estimate the price of a share of stock five weeks ago.
Skills PracticeWriting Equations in Slope-Intercept Form
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Chapter 4 14 Glencoe Algebra 1
PracticeWriting Equations in Slope-Intercept Form
Write an equation of the line that passes through the given point and has the given slope.
1.
(1, 2)
x
y
O
m = 3
2.
(–2, 2)
x
y
O
m = –2
3.
(–1, –3)
x
y
O
m = –1
4. (-5, 4); slope -3 5. (4, 3); slope 1 −
2 6. (1, -5); slope -
3 −
2
7. (3, 7); slope 2 −
7 8.
(
-2, 5 −
2 )
; slope -
1 −
2 9. (5, 0); slope 0
Write an equation of the line that passes through each pair of points.
10.
(4, –2)
(2, –4)
x
y
O
11. (0, 5)
(4, 1)x
y
O
12. (–3, 1)
(–1, –3)
x
y
O
13. (0, -4), (5, -4) 14. (-4, -2), (4, 0) 15. (-2, -3), (4, 5)
16. (0, 1), (5, 3) 17. (-3, 0), (1, -6) 18. (1, 0), (5, -1)
19. DANCE LESSONS The cost for 7 dance lessons is $82. The cost for 11 lessons is $122. Write a linear equation to find the total cost C for ℓ lessons. Then use the equation to find the cost of 4 lessons.
20. WEATHER It is 76°F at the 6000-foot level of a mountain, and 49°F at the 12,000-foot level of the mountain. Write a linear equation to find the temperature T at an elevation x on the mountain, where x is in thousands of feet.
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Chapter 4 15 Glencoe Algebra 1
Word Problem PracticeWriting Equations in Slope-Intercept Form
1. FUNDRAISING Yvonne and her friends held a bake sale to benefit a shelter for homeless people. The friends sold 22 cakes on the first day and 15 cakes on the second day of the bake sale. They collected $88 on the first day and $60 on the second day. Let x represent the number of cakes sold and y represent the amount of money made. Find the slope of the line that would pass through the points given.
2. JOBS Mr. Kimball receives a $3000 annual salary increase on the anniversary of his hiring if he receives a satisfactory performance review. His starting salary was $41,250. Write an equation to show k, Mr. Kimball’s salary after t years at this company if his performance reviews are always satisfactory.
3. CENSUS The population of Laredo, Texas, was about 215,500 in 2007. It was about 123,000 in 1990. If we assume that the population growth is constant and t represents the number of years after 1990, write a linear equation to find p, Laredo’s population for any year after 1990.
4. WATER Mr. Williams pays $40 a month for city water, no matter how many gallons of water he uses in a given month. Let x represent the number of gallons of water used per month. Let yrepresent the monthly cost of the city water in dollars. What is the equation of the line that represents this information? What is the slope of the line?
5. SHOE SIZES The table shows how women’s shoe sizes in the United Kingdom compare to women’s shoe sizes in the United States.
Women’s Shoe Sizes
U.K. 3 3.5 4 4.5 5 5.5 6
U.S. 5.5 6 6.5 7 7.5 8 8.5
Source: DanceSport UK
a. Write a linear equation to determine any U.S. size y if you are given the U.K. size x.
b. What are the slope and y-intercept of the line?
c. Is the y-intercept a valid data point for the given information?
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Chapter 4 16 Glencoe Algebra 1
Tangent to a CurveA tangent line is a line that intersects a curve at a point with the same rate of change, or slope, as the rate of change of the curve at that point.
For quadratic functions, functions of the form y = ax2 + bx + c, equations of the tangent lines
can be found. This is based on the fact that the slope through any two points on the curve is equal to the slope of the line tangent to the curve at the point whose x-value is halfway between the x-values of the other two points.
Find an equation of the line tangent to the curve y = x2 + 3x + 2 through the point (2, 12).
First find two points on the curve whose x-values are equidistant from the x-value of (2, 12).
Step 1: Find two points on the curve. Use x = 1 and x = 3. When x = 1, y = 12 + 3(1) + 2 or 6. When x = 3, y = 32 + 3(3) + 2 or 20. So, the two ordered pairs are (1, 6) and (3, 20).
Step 2: Find the slope of the line that passes through these two points. m = 20 - 6 −
3 - 1 or 7
Step 3: Now use this slope and the point (2, 12) to find an equation of the tangent line. y = mx + b Slope-intercept form
12 = 7(2) + b Replace x with 2, y with 12, and m with 7.
-2 = b Solve for b.
So, an equation of the tangent line to y = x2 + 3x + 2 through the point (2, 12) is y = 7x – 2.
ExercisesFind an equation of the line tangent to each curve through the given point.
1. y = x2 - 3x + 7, (2, 5) 2. y = 3x2 + 4x - 5, (-4, 27) 3. y = 5 - x2, (1, 4)
4. Find the slope of the line tangent to the curve at x = 0 for the general equation y = ax2 + bx + c.
5. Find the slope of the line tangent to the curve y = ax2 + bx + c at x by finding the slope of the line through the points (0, c) and (2x, 4ax2 + 2bx + c). Does this equation find the same slope for x = 0 as you found in Exercise 4?
Enrichment
y
xO
Example
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Chapter 4 17 Glencoe Algebra 1
Study Guide and InterventionWriting Equations in Point-Slope Form
Point-Slope Form
Point-Slope Formy - y
1 = m(x - x
1), where (x
1, y
1) is a given point on a nonvertical line
and m is the slope of the line
Write an equation in point-slope form for the line that passes through (6, 1) with a slope of -
5 −
2 .
y - y1 = m(x - x1) Point-slope form
y - 1 = -
5 −
2 (x - 6) m = - 5 −
2 ; (x
1, y
1) = (6, 1)
Therefore, the equation is y - 1 = -
5 −
2 (x - 6).
Write an equation in point-slope form for a horizontal line that passes through (4, -1).
y - y1 = m(x - x1) Point-slope form
y - (-1) = 0(x - 4) m = 0; (x1, y
1) = (4, -1)
y + 1 = 0 Simplify.
Therefore, the equation is y + 1 = 0.
ExercisesWrite an equation in point-slope form for the line that passes through each point with the given slope.
1. (4, 1)
x
y
O
m = 1
2.
(–3, 2)
x
y
O
m = 0 3.
(2, –3)
x
y
O
m = –2
4. (2, 1), m = 4 5. (-7, 2), m = 6 6. (8, 3), m = 1
7. (-6, 7), m = 0 8. (4, 9), m = 3 −
4 9. (-4, -5), m = -
1 −
2
10. Write an equation in point-slope form for a horizontal line that passes through (4, -2).
11. Write an equation in point-slope form for a horizontal line that passes through (-5, 6).
12. Write an equation in point-slope form for a horizontal line that passes through (5, 0).
Example 1 Example 2
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Chapter 4 18 Glencoe Algebra 1
Study Guide and Intervention (continued)
Writing Equations in Point-Slope Form
Forms of Linear EquationsSlope-Intercept
Formy = mx + b m = slope; b = y-intercept
Point-Slope Form
y - y1 = m(x - x
1) m = slope; (x
1, y
1) is a given point
Standard
FormAx + By = C
A and B are not both zero. Usually A is nonnegative and A, B, and
C are integers whose greatest common factor is 1.
Write y + 5 = 2 −
3 (x - 6) in
standard form.
y + 5 = 2 −
3 (x - 6) Original equation
3(y + 5) = 3 ( 2 −
3 ) (x - 6) Multiply each side by 3.
3y + 15 = 2(x - 6) Distributive Property
3y + 15 = 2x - 12 Distributive Property
3y = 2x - 27 Subtract 15 from each side.
-2x + 3y = -27 Add -2x to each side.
2x - 3y = 27 Multiply each side by -1.
Therefore, the standard form of the equation is 2x - 3y = 27.
Write y - 2 = - 1 −
4 (x - 8) in
slope-intercept form.
y - 2 = -
1 −
4 (x - 8) Original equation
y - 2 = -
1 −
4 x + 2 Distributive Property
y = -
1 −
4 x + 4 Add 2 to each side.
Therefore, the slope-intercept form of the equation is y = -
1 −
4 x + 4.
ExercisesWrite each equation in standard form.
1. y + 2 = -3(x - 1) 2. y - 1 = -
1 −
3 (x - 6) 3. y + 2 = 2 −
3 (x - 9)
4. y + 3 = -(x - 5) 5. y - 4 = 5 −
3 (x + 3) 6. y + 4 = -
2 −
5 (x - 1)
Write each equation in slope-intercept form.
7. y + 4 = 4(x - 2) 8. y - 5 = 1 −
3 (x - 6) 9. y - 8 = -
1 −
4 (x + 8)
10. y - 6 = 3 (x - 1 −
3 ) 11. y + 4 = -2(x + 5) 12. y + 5 −
3 = 1 −
2 (x - 2)
Example 1 Example 2
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Chapter 4 19 Glencoe Algebra 1
Skills PracticeWriting Equations in Point-Slope Form
Write an equation in point-slope form for the line that passes through each point with the given slope.
1.
(–1, –2)x
y
O
m = 3
2.
(1, –2)x
y
O
m = –1 3.
(2, –3)
x
y
O
m = 0
4. (3, 1), m = 0 5. (-4, 6), m = 8 6. (1, -3), m = -4
7. (4, -6), m = 1 8. (3, 3), m = 4 −
3 9. (-5, -1), m = -
5 −
4
Write each equation in standard form.
10. y + 1 = x + 2 11. y + 9 = -3(x - 2) 12. y - 7 = 4(x + 4)
13. y - 4 = -(x - 1) 14. y - 6 = 4(x + 3) 15. y + 5 = -5(x - 3)
16. y - 10 = -2(x - 3) 17. y - 2 = -
1 −
2 (x - 4) 18. y + 11 = 1 −
3 (x + 3)
Write each equation in slope-intercept form.
19. y - 4 = 3(x - 2) 20. y + 2 = -(x + 4) 21. y - 6 = -2(x + 2)
22. y + 1 = -5(x - 3) 23. y - 3 = 6(x - 1) 24. y - 8 = 3(x + 5)
25. y - 2 = 1 −
2 (x + 6) 26. y + 1 = -
1 −
3 (x + 9) 27. y - 1 −
2 = x + 1 −
2
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Chapter 4 20 Glencoe Algebra 1
PracticeWriting Equations in Point-Slope Form
Write an equation in point-slope form for the line that passes through each point with the given slope.
1. (2, 2), m = -3 2. (1, -6), m = -1 3. (-3, -4), m = 0
4. (1, 3), m = -
3 −
4 5. (-8, 5), m = -
2 −
5 6. (3, -3), m = 1 −
3
Write each equation in standard form.
7. y - 11 = 3(x - 2) 8. y - 10 = -(x - 2) 9. y + 7 = 2(x + 5)
10. y - 5 = 3 −
2 (x + 4) 11. y + 2 = -
3 −
4 (x + 1) 12. y - 6 = 4 −
3 (x - 3)
13. y + 4 = 1.5(x + 2) 14. y - 3 = -2.4(x - 5) 15. y - 4 = 2.5(x + 3)
Write each equation in slope-intercept form.
16. y + 2 = 4(x + 2) 17. y + 1 = -7(x + 1) 18. y - 3 = -5(x + 12)
19. y - 5 = 3 −
2 (x + 4) 20. y - 1 −
4 = - 3 (x + 1 −
4 ) 21. y - 2 −
3 = -2 (x - 1 −
4 )
22. CONSTRUCTION A construction company charges $15 per hour for debris removal, plus a one-time fee for the use of a trash dumpster. The total fee for 9 hours of service is $195.
a. Write the point-slope form of an equation to find the total fee y for any number of hours x.
b. Write the equation in slope-intercept form.
c. What is the fee for the use of a trash dumpster?
23. MOVING There is a daily fee for renting a moving truck, plus a charge of $0.50 per mile driven. It costs $64 to rent the truck on a day when it is driven 48 miles.
a. Write the point-slope form of an equation to find the total charge y for a one-day rental with x miles driven.
b. Write the equation in slope-intercept form.
c. What is the daily fee?
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Chapter 4 21 Glencoe Algebra 1
1. BICYCLING Harvey rides his bike at an average speed of 12 miles per hour. In other words, he rides 12 miles in 1 hour, 24 miles in 2 hours, and so on. Let h be the number of hours he rides and d be distance traveled. Write an equation for the relationship between distance and time in point-slope form.
2. GEOMETRY The perimeter of a square varies directly with its side length. The point-slope form of the equation for this function is y - 4 = 4(x - 1). Write the equation in standard form.
3. NATURE The frequency of a male cricket’s chirp is related to the outdoor temperature. The relationship is expressed by the equation T = n + 40, where T is the temperature in degrees Fahrenheit and n is the number of chirps the cricket makes in 14 seconds. Use the information from the graph below to write an equation for the line in point-slope form .
Number of Chirps151050 2520
y
x30 35
Tem
per
atu
re (
°F)
30
40
20
10
50
70
60
4. CANOEING Geoff paddles his canoe at an average speed of 3.5 miles per hour. After 5 hours of canoeing, Geoff has traveled 18 miles. Write an equation in point-slope form to find the total distance y for any number of hours x.
5. AVIATION A jet plane takes off and consistently climbs 20 feet for every 40 feet it moves horizontally. The graph shows the trajectory of the jet.
Horizontal Distance (ft)
5000 1000 1500 2000 2500
Hei
gh
t (f
t)600
800
400
200
1000
1400
1200
a. Write an equation in point-slope form for the line representing the jet’s trajectory.
b. Write the equation from part a in slope -intercept form.
c. Write the equation in standard form.
Word Problem PracticeWriting Equations in Point-Slope Form
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Chapter 4 22 Glencoe Algebra 1
Enrichment
x
y
O
x
y
O
Collinearity You have learned how to find the slope between two points on a line. Does it matter which two points you use? How does your choice of points affect the slope-intercept form of the equation of the line?
1. Choose three different pairs of points from the graph at the right. Write the slope-intercept form of the line using each pair.
2. How are the equations related?
3. What conclusion can you draw from your answers to Exercises 1 and 2?
When points are contained in the same line, they are said to be collinear. Even though points may look like they form a line when connected, it doesnot mean that they actually do. By checking pairs of points on a graph you can determine whether the graph represents a linear relationship.
4. Choose several pairs of points from the graph at the right and write the slope-intercept form of the line containingeach pair.
5. What conclusion can you draw from your equations in Exercise 4? Is this a line?
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Chapter 4 23 Glencoe Algebra 1
Graphing Calculator ActivityWriting Linear Equations
Lists can be used with the linear regression function to write and verify linear equations given two points on a line, or the slope of a line and a point through which it passes. The linear regression function, LinReg (ax + b), is found under the STAT CALC menu.
Write the slope-intercept form of an equation of the line that passes through (3, -2) and (6, 4).
Enter the x-coordinates of the points into L1 and the y-coordinates into L2. Use the linear regression function to write the equation of the line.
Keystrokes: STAT ENTER 3 ENTER 6 ENTER (–) 2 ENTER 4 ENTER STAT 4 2nd [L1] , 2nd [L2] ENTER .
The equation is y = 2x - 8.
If you have already written the equation of a line, you can use the given information to verify your equation.
ExercisesWrite the slope-intercept form and the standard form of an equation of the line that satisfies each condition.
1. passes through (0, 7) and ( 1 −
7 , -5) 2. passes through (-5, 1), (10, 10), and (-10, -2)
3. passes through (6, -4), m = 2 −
3 4. passes through (3, 5), m = -4
5. x-intercept: 1, y-intercept: -
1 −
2 6. passes through (-18, 11), y-intercept: 3
Verify that the equation of the line passing through (2, -3) with slope -
3 −
4 can be written as 3x + 4y = -6.
Use the given point and slope to determine a second point through which the line passes. Enter the x-coordinates of the points into L1 and the y-coordinates into L2. Use LinReg (ax + b) to determine the slope-intercept form of the equation.
The slope-intercept form of the equation is y = -0.75x - 1.5 or y = -
3 −
4 x - 3 −
2 .
This can be rewritten in standard form as 3x + 4y = -6.
Example 1
Example 2
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Chapter 4 24 Glencoe Algebra 1
Study Guide and InterventionParallel and Perpendicular Lines
Parallel Lines Two nonvertical lines are parallel if they have the same slope. All vertical lines are parallel.
Write an equation in slope-intercept form for the line that passes through (-1, 6) and is parallel to the graph of y = 2x + 12.
A line parallel to y = 2x + 12 has the same slope, 2. Replace m with 2 and (x1, y1) with (-1, 6) in the point-slope form. y - y1 = m(x - x1) Point-slope form
y - 6 = 2(x - (-1)) m = 2; (x1, y
1) = (-1, 6)
y - 6 = 2(x + 1) Simplify.
y - 6 = 2x + 2 Distributive Property
y = 2x + 8 Slope-intercept form
Therefore, the equation is y = 2x + 8.
ExercisesWrite an equation in slope-intercept form for the line that passes through the given point and is parallel to the graph of each equation.
1. 2. 3.
4. (-2, 2), y = 4x - 2 5. (6, 4), y = 1 −
3 x + 1 6. (4, -2), y = -2x + 3
7. (-2, 4), y = -3x + 10 8. (-1, 6), 3x + y = 12 9. (4, -6), x + 2y = 5
10. Find an equation of the line that has a y-intercept of 2 that is parallel to the graph of the line 4x + 2y = 8.
11. Find an equation of the line that has a y-intercept of -1 that is parallel to the graph of the line x - 3y = 6.
12. Find an equation of the line that has a y-intercept of -4 that is parallel to the graph of the line y = 6.
(–3, 3)
x
y
O
4x - 3y = –12
(-8, 7)
x
y
O
y = - x - 412
2
2
(5, 1)x
y
O
y = x - 8
Example
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Chapter 4 25 Glencoe Algebra 1
Study Guide and Intervention (continued)
Parallel and Perpendicular Lines
Perpendicular Lines Two nonvertical lines are perpendicular if their slopes are negative reciprocals of each other. Vertical and horizontal lines are perpendicular.
Write an equation in slope-intercept form for the line that passes through (-4, 2) and is perpendicular to the graph of 2x - 3y = 9.
Find the slope of 2x - 3y = 9. 2x - 3y = 9 Original equation
-3y = -2x + 9 Subtract 2x from each side.
y = 2 −
3 x - 3 Divide each side by -3.
The slope of y = 2 −
3 x - 3 is 2 −
3 . So, the slope of the line passing through (-4, 2) that is
perpendicular to this line is the negative reciprocal of 2 −
3 , or -
3 −
2 .
Use the point-slope form to find the equation.y - y1 = m(x - x1) Point-slope form
y - 2 = -
3 −
2 (x - (-4)) m = -
3 −
2 ; (x
1, y
1) = (-4, 2)
y - 2 = -
3 −
2 (x + 4) Simplify.
y - 2 = -
3 −
2 x - 6 Distributive Property
y = -
3 −
2 x - 4 Slope-intercept form
Exercises 1. ARCHITECTURE On the architect’s plans for a new high school, a wall represented
by −−−
MN has endpoints M(-3, -1) and N(2, 1). A wall represented by −−−
PQ has endpoints P(4, -4) and Q(-2, 11). Are the walls perpendicular? Explain.
Determine whether the graphs of the following equations are parallel or perpendicular.
2. 2x + y = -7, x - 2y = -4, 4x - y = 5
3. y = 3x, 6x - 2y = 7, 3y = 9x - 1
Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the graph of each equation.
4. (4, 2), y = 1 −
2 x + 1 5. (2, -3), y = -
2 −
3 x + 4 6. (6, 4), y = 7x + 1
7. (-8, -7), y = -x - 8 8. (6, -2), y = -3x - 6 9. (-5, -1), y = 5 −
2 x - 3
Example
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Chapter 4 26 Glencoe Algebra 1
Skills PracticeParallel and Perpendicular Lines
Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the graph of the given equation.
1. 2. 3.
4. (3, 2), y = 3x + 4 5. (-1, -2), y = -3x + 5 6. (-1, 1), y = x - 4
7. (1, -3), y = -4x - 1 8. (-4, 2), y = x + 3 9. (-4, 3), y = 1 −
2 x - 6
10. RADAR On a radar screen, a plane located at A(-2, 4) is flying toward B(4, 3).
Another plane, located at C(-3, 1), is flying toward D(3, 0). Are the planes’ paths perpendicular? Explain.
Determine whether the graphs of the following equations are parallel or perpendicular. Explain.
11. y = 2 −
3 x + 3, y = 3 −
2 x, 2x - 3y = 8
12. y = 4x, x + 4 y = 12, 4x + y = 1
Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the graph of the given equation.
13. (-3, -2), y = x + 2 14. (4, -1), y = 2x - 4 15. (-1, -6), x + 3y = 6
16. (-4, 5), y = -4x - 1 17. (-2, 3), y =
1 −
4 x - 4 18. (0, 0), y =
1 −
2 x - 1
(–2, 2)
x
y
O
y = 12 x + 1(1, –1)
x
y
O
y = –x + 3
(–2, –3)
x
y
O
y = 2x - 1
4-4
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Chapter 4 27 Glencoe Algebra 1
Practice Parallel and Perpendicular Lines
Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the graph of the given equation.
1. (3, 2), y = x + 5 2. (-2, 5), y = -4x + 2 3. (4, -6), y = -
3
−
4
x + 1
4. (5, 4), y = 2 −
5 x - 2 5. (12, 3), y = 4 −
3 x + 5 6. (3, 1), 2x + y = 5
7. (-3, 4), 3y = 2x - 3 8. (-1, -2), 3x - y = 5 9. (-8, 2), 5x - 4y = 1
10. (-1, -4), 9x + 3y = 8 11. (-5, 6), 4x + 3y = 1 12. (3, 1), 2x + 5y = 7
Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the graph of the given equation.
13. (-2, -2), y = -
1
−
3
x + 9 14. (-6, 5), x - y = 5 15. (-4, -3), 4x + y = 7
16. (0, 1), x + 5y = 15 17. (2, 4), x - 6y = 2 18. (-1, -7), 3x + 12y = -6
19. (-4, 1), 4x + 7y = 6 20. (10, 5), 5x + 4y = 8 21. (4, -5), 2x - 5y = -10
22. (1, 1), 3x + 2y = -7 23. (-6, -5), 4x + 3y = -6 24. (-3, 5), 5x - 6y = 9
25. GEOMETRY Quadrilateral ABCD has diagonals −−
AC and −−−
BD . Determine whether
−−
AC is perpendicular to −−−
BD . Explain.
26. GEOMETRY Triangle ABC has vertices A(0, 4), B(1, 2), and C(4, 6). Determine whether triangle ABC is a right triangle. Explain.
x
y
O
A
D
C
B
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Chapter 4 28 Glencoe Algebra 1
1. BUSINESS Brady’s Books is a retail store. The store’s average daily profits y are given by the equation y = 2x + 3 where x is the number of hours available for customer purchases. Brady’s adds an online shopping option. Write an equation in slope-intercept form to show a new profit line with the same profit rate containing the point (0, 12).
2. ARCHITECTURE The front view of a house is drawn on graph paper. The left side of the roof of the house is represented by the equation y = x. The rooflines intersect at a right angle and the peak of the roof is represented by the point (5, 5). Write the equation in slope-intercept form for the line that creates the right side of the roof.
3. ARCHAEOLOGY An archaeologist is comparing the location of a jeweled box she just found to the location of a brick wall. The wall can be represented by the
equation y = -
5 −
3 x + 13. The box is
located at the point (10, 9). Write an equation representing a line that is perpendicular to the wall and that passes through the location of the box.
4. GEOMETRY A parallelogram is created by the intersections of the lines x = 2,
x = 6, y = 1 −
2 x + 2, and another line. Find
the equation of the fourth line needed to complete the parallelogram. The line should pass through (2, 0). (Hint: Sketch a graph to help you see the lines.)
5. INTERIOR DESIGN Pamela is planning to install an island in her kitchen. She draws the shape she likes by connecting the vertices of the square tiles on her kitchen floor. She records the location of each corner in the table.
a. How many pairs of parallel sides are there in the shape ABCD she designed? Explain.
b. How many pairs of perpendicular sides are there in the shape she designed? Explain.
c. What is the shape of her new island?
Word Problem PracticeParallel and Perpendicular Lines
y
xO
(5, 5)
Corner
Distance
from West
Wall (tiles)
Distance
from South
Wall (tiles)
A 5 4
B 3 8
C 7 10
D 11 7
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Chapter 4 29 Glencoe Algebra 1
Enrichment
Pencils of LinesAll of the lines that pass through a single point in the same plane are called a pencil of lines.All lines with the same slope, but different intercepts, are also called a “pencil,” a pencil of parallel lines.
Graph some of the lines in each pencil.
1. A pencil of lines through the 2. A pencil of lines described by point (1, 3) y - 4 = m(x - 2), where m is any
real number
3. A pencil of lines parallel to the line 4. A pencil of lines described by x - 2y = 7 y = mx + 3m - 2 , where m is any
real number
x
y
Ox
y
O
x
y
Ox
y
O
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Chapter 4 30 Glencoe Algebra 1
Study Guide and InterventionScatter Plots and Lines of Fit
Investigate Relationships Using Scatter Plots A scatter plot is a graph in which two sets of data are plotted as ordered pairs in a coordinate plane. If y increases as x increases, there is a positive correlation between x and y. If y decreases as x increases, there is a negative correlation between x and y. If x and y are not related, there is no correlation.
EARNINGS The graph at the right shows the amount of money Carmen earned each week and the amount she deposited in her savings account that same week. Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation.
The graph shows a positive correlation. The more Carmen earns, the more she saves.
ExercisesDetermine whether each graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation.
1. 2.
3. 4.
Average Weekly Work Hours in U.S.
Hour
s
34.0
34.2
33.8
33.6
34.4
34.6
Years Since 19953210 54 76 98
Source: The World Almanac
Average Jogging Speed
Minutes
Mile
s pe
r Hou
r
0 10 205 15 25
10
5
Carmen’s Earnings and Savings
Dollars Earned
Dolla
rs S
aved
0 40 80 120
35
30
25
20
15
10
5
Example
Average U.S. HourlyEarnings
Hour
ly E
arni
ngs
($)
15
0
16
17
18
19
Years Since 2003Source: U.S. Dept. of Labor
1 2 3 4 5
U.S. Imports from Mexico
Impo
rts
($ b
illio
ns)
130
0
160
190
220
Years Since 2003Source: U.S. Census Bureau
1 2 3 4 5
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Chapter 4 31 Glencoe Algebra 1
Use Lines of Fit
The table shows the number of students per computer in Easton High School for certain school years from 1996 to 2008.
Year 1996 1998 2000 2002 2004 2006 2008
Students per Computer 22 18 14 10 6.1 5.4 4.9
a. Draw a scatter plot and determine what relationship exists, if any.Since y decreases as x increases, the correlation is negative.
b. Draw a line of fit for the scatter plot.Draw a line that passes close to most of the points. A line of fit is shown.
c. Write the slope-intercept form of an equation for the line of fit.The line of fit shown passes through (1999, 16) and (2005, 5.7). Find the slope.
m = 5.7 - 16
−
2005 - 1999
m = -1.7 Find b in y = -1.7x + b. 16 = -1.7 · 1993 + b 3404 = b Therefore, an equation of a line of fit is y = -1.7x + 3404.
ExercisesRefer to the table for Exercises 1–3.
1. Draw a scatter plot.
2. Draw a line of fit for the data.
3. Write the slope-interceptform of an equation for the line of fit.
Movie Admission Prices
Adm
issi
on ($
)
5.4
5.6
5.2
5
5.8
6
6.2
Years Since 19993210 54
Source: U.S. Census Bureau
Study Guide and Intervention (continued)
Scatter Plots and Lines of Fit
Students per Computerin Easton High School
Stud
ents
per
Com
pute
r
81216
4
0
2024
Year1996 1998 2000 2002 2004 2006 2008
Example
Years
Since 1999
Admission
(dollars)
0 $5.08
1 $5.39
2 $5.66
3 $5.81
4 $6.03
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Chapter 4 32 Glencoe Algebra 1
Skills PracticeScatter Plots and Lines of Fit
Determine whether each graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation.
1. 2.
3. 4.
5. BASEBALL The scatter plot shows the average price of a major-league baseball ticket from 1997 to 2006.
a. Determine what relationship, if any, exists in the data. Explain.
b. Use the points (1998, 13.60) and (2003, 19.00) to write the slope-intercept form of an equation for the line of fit shown in the scatter plot.
c. Predict the price of a ticket in 2009.
Weight-Lifting
Weight (pounds)
Repe
titio
ns
0 40 8020 60 100 120 140
14
12
10
8
6
4
2
Library Fines
Books Borrowed
Fine
s (d
olla
rs)
0 2 4 5 6 7 8 91 3 10
7
6
5
4
3
2
1
Calories BurnedDuring Exercise
Time (minutes)
Calo
ries
0 20 4010 30 50 60
600
500
400
300
200
100
Baseball Ticket Prices
Aver
age
Pric
e ($
)
14
16
12
0
18
20
22
24
Year’99’98’97 ’01 ’03’00
Source: Team Marketing Report, Chicago
’02 ’04 ’05 ’06
Car Dealership Revenue
Reve
nue
(hun
dred
s of
thou
sand
s)
4
6
2
0
8
10
12
14
Year’99 ’01 ’03’00 ’02 ’04 ’05 ’06 ’07 ’08
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Chapter 4 33 Glencoe Algebra 1
Practice Scatter Plots and Lines of Fit
Determine whether each graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation.
1. 2.
3. DISEASE The table shows the number of cases of Foodborne Botulism in the United States for the years 2001 to 2005.
a. Draw a scatter plot and determine what relationship, if any, exists in the data.
b. Draw a line of fit for the scatter plot.
c. Write the slope-intercept form of an equation for the
line of fit.
4. ZOOS The table shows the average and maximum longevity of various animals in captivity.
a. Draw a scatter plot and determine what relationship, if any, exists in the data.
b. Draw a line of fit for the scatter plot.
c. Write the slope-intercept form of an equation for the line of fit.
d. Predict the maximum longevity for an animal with an average longevity of 33 years.
State Elevations
Mean Elevation (feet)
High
est P
oint
(thou
sand
s of
feet
)
10000 2000 3000
16
12
8
4
Source: U.S. Geological Survey
Temperature versus Rainfall
Average Annual Rainfall (inches)
Aver
age
Tem
pera
ture
(ºF)
10 15 20 25 30 35 40 45
64
60
56
52
0
Source: National Oceanic and AtmosphericAdministration
U.S. FoodborneBotulism Cases
Case
s
20
30
10
0
40
50
Year2001 2002 2003 2004 2005
Animal Longevity (Years)
Average
Max
imum
50 10 15 20 25 30 35 40 45
80
70
60
50
40
30
20
10
Source: Centers for Disease Control
U.S. Foodborne Botulism Cases
Year 2001 2002 2003 2004 2005
Cases 39 28 20 16 18
Source: Walker’s Mammals of the World
Longevity (years)
Avg. 12 25 15 8 35 40 41 20
Max. 47 50 40 20 70 77 61 54
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Chapter 4 34 Glencoe Algebra 1
1. MUSIC The scatter plot shows the number of CDs in millions that were sold from 1999 to 2005. If the trend continued, about how many CDs were sold in 2006?
2. FAMILY The table shows the predicted annual cost for a middle income family to raise a child from birth until adulthood. Draw a scatter plot and describe what relationship exists within the data.
3. HOUSING The median price of an existing home was $160,000 in 2000 and $240,000 in 2007. If x represents the number of years since 2000, use these data points to determine a line of best fit for the trends in the price of existing homes. Write the equation in slope-intercept form.
4. BASEBALL The table shows the average length in minutes of professional baseball games in selected years.
Source: Elias Sports Bureau
a. Draw a scatter plot and determine what relationship, if any, exists in the data.
b. Explain what the scatter plot shows.
c. Draw a line of fit for the scatter plot.
Tim
e (m
in)
166
0
168
170
172
174
176
178
180
Year’90 ’92 ’94 ’96 ’98 ’00 ’02
Age (years)30 6 12 15
y
x9
An
nu
al C
ost
($1
000)
11
12
10
9
13
16
15
14
17
Source: The World Almanac
Source: RIAA
Year‘01‘00‘990 ‘03‘02 ‘05
y
x‘04
CD
s (m
illio
ns)
750
800
700
650
850
950
900
Word Problem PracticeScatter Plots and Lines of Fit
Cost of Raising a Child Born in 2003
Child’s
Age3 6 9 12 15
Annual
Cost ($)10,700 11,700 12,600 15,000 16,700
Average Length of
Major League Baseball Games
Year ‘92 ‘94 ‘96 ‘98 ‘00 ‘02 ‘04
Time (min) 170 174 171 168 178 172 167
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Chapter 4 35 Glencoe Algebra 1
Enrichment
Latitude and Temperature
The latitude of a place on Earth is the measure of its distance fromthe equator. What do you think is the relationship between a city’s latitude and its mean January temperature? At the right is a table containing the latitudes and January mean temperatures for fifteen U.S. cities.
Sources: National Weather Service
1. Use the information in the table to create a scatter plot and draw a line of best fit for the data.
2. Write an equation for the line of fit. Make a conjecture about the relationship between a city’s latitude and its mean January temperature.
3. Use your equation to predict the January mean temperature of Juneau, Alaska, which has latitude 58:23 N.
4. What would you expect to be the latitude of a city with a January mean temperature of 15°F?
5. Was your conjecture about the relationship between latitude and temperature correct?
6. Research the latitudes and temperatures for cities in the southern hemisphere. Does your conjecture hold for these cities as well?
Latitude (ºN)
Tem
per
atu
re (
ºF)
70
60
50
40
30
20
10
0
-10
T
L20 40 6010 30 50
U.S. City Latitude January Mean Temperature
Albany, New York 42:40 N 20.7°F
Albuquerque, New Mexico 35:07 N 34.3°F
Anchorage, Alaska 61:11 N 14.9°F
Birmingham, Alabama 33:32 N 41.7°F
Charleston, South Carolina 32:47 N 47.1°F
Chicago, Illinois 41:50 N 21.0°F
Columbus, Ohio 39:59 N 26.3°F
Duluth, Minnesota 46:47 N 7.0°F
Fairbanks, Alaska 64:50 N -10.1°F
Galveston, Texas 29:14 N 52.9°F
Honolulu, Hawaii 21:19 N 72.9°F
Las Vegas, Nevada 36:12 N 45.1°F
Miami, Florida 25:47 N 67.3°F
Richmond, Virginia 37:32 N 35.8°F
Tucson, Arizona 32:12 N 51.3°F
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Chapter 4 36 Glencoe Algebra 1
ExercisesThe table shows the number of millions of dollars of direct political contributions received by Democrats and Republicansin selected years.1. Use a spreadsheet to draw a scatter plot and a trendline for the
data. Let x represent the number of years since 1990 and let y represent direct political contributions in millions of dollars.
2. Predict the amount of direct political contributions for the 2010 election.
Spreadsheet ActivityScatter Plots
The table below shows the number of metric tons of gold produced in mines in the United States in selected years.
Use a spreadsheet to draw a scatter plot and a trendline for the data. Let x represent the number of years since 2000 and let y represent the number of metric tons of gold. Then predict the number of ounces of gold produced in 2013.
Step 1 Use Column A for the years since 2000 and Column B for the number of metric tons of gold. To create a graph from the data, select the data in Columns A and B and choose Chart from the Insert menu. Select an XY (Scatter) chart to show the data points.
Step 2 Add a trendline to the graph by choosing the Chart menu. Add a linear trendline. Use the options menu to have the trendline forecast 5 years forward.
Using this trendline, it appears that the gold production for 2013 will be approximately 150 metric tons.
A spreadsheet program can create scatter plots of data that you enter. You can also have the spreadsheet graph a line of fit, called a trendline, automatically.
Example
Source: Open Secrets
Year Contributions
1990 281
1994 337
1998 445
2002 717
2006 1085
Source: U.S. Geological Survey
Year 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009
Gold 353 335 298 277 247 256 252 238 233 210
4-5
A1 0
12
34
5
6
78
9
353335298
277247
256
252
238233
210
34567891011121314
2
B C D E F G H
15
Spreadsheet sample
Sheet 1 Sheet 2 Sheet 3
U.S. Gold Mine Production
Gold
(met
ric to
ns)
100
150
50
0
200
250
300
350
400
Years since 20005 10 15
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Chapter 4 37 Glencoe Algebra 1
Equations of Best-Fit Lines Many graphing calculators utilize an algorithm called linear regression to find a precise line of fit called the best-fit line. The calculator computes the data, writes an equation, and gives you the correlation coefficent, a measure of how closely the equation models the data.
GAS PRICES The table shows the price of a gallon of regular gasoline at a station in Los Angeles, California on January 1 of various years. Year 2005 2006 2007 2008 2009 2010
Average Price $1.47 $1.82 $2.15 $2.49 $2.83 $3.04
Source: U.S. Department of Energy
a. Use a graphing calculator to write an equation for the best-fit line for that data. Enter the data by pressing STAT and selecting the Edit option. Let the year 2005 be represented by 0. Enter the years since 2005 into List 1 (L1). Enter the average price into List 2 (L2).
Then, perform the linear regression by pressing STAT and selecting the CALC option. Scroll down to LinReg (ax+b) and press ENTER . The best-fit equation for the regression is shown to be y = 0.321x + 1.499.
b. Name the correlation coefficient. The correlation coefficient is the value shown for r on the calculator screen. The correlation coefficient is about 0.998.
ExercisesWrite an equation of the regression line for the data in each table below. Then find the correlation coefficient.
1. OLYMPICS Below is a table showing the number of gold medals won by the United States at the Winter Olympics during various years.
Year 1992 1994 1998 2002 2006 2010
Gold Medals 5 6 6 10 9 9
Source: International Olympic Committee
2. INTEREST RATES Below is a table showing the U.S. Federal Reserve’s prime interest rate on January 1 of various years.
Year 2006 2007 2008 2009 2010
Prime Rate (percent) 7.25 8.25 7.25 3.25 3.25
Source: Federal Reserve Board
Study Guide and InterventionRegression and Median-Fit Lines
Example
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Chapter 4 38 Glencoe Algebra 1
Equations of Median-Fit Lines A graphing calculator can also find another type of best-fit line called the median-fit line, which is found using the medians of the coordinates of the data points.
ELECTIONS The table shows the total number of people in millions who voted in the U.S. Presidential election in the given years.
Year 1980 1984 1988 1992 1996 2004 2008
Voters 86.5 92.7 91.6 104.4 96.3 122.3 131.3
Source: George Mason University
a. Find an equation for the median-fit line. Enter the data by pressing STAT and selecting the Edit option. Let the year 1980 be represented by 0. Enter the years since 1980 into List 1 (L1). Enter the number of voters into List 2 (L2).
Then, press STAT and select the CALC option. Scroll down to Med-Med option and press ENTER . The value of a is the slope, and the value of b is the y-intercept.The equation for the median-fit line is y = 1.55x + 83.57.
b. Estimate the number of people who voted in the 2000 U.S. Presidential election. Graph the best-fit line. Then use the
TRACE feature and the arrow keys until you find a point where x = 20.
When x = 20, y ≈ 115. Therefore, about 115 million people voted in the 2000 U.S. Presidential election.
ExercisesWrite an equation of the regression line for the data in each table below. Then find the correlation coefficient.
1. POPULATION GROWTH Below is a table showing the estimated population of Arizona in millions on July 1st of various years.
Year 2001 2002 2003 2004 2005 2006
Population 5.30 5.44 5.58 5.74 5.94 6.17
Source: U.S. Census Bureau
a. Find an equation for the median-fit line.
b. Predict the population of Arizona in 2009.
2. ENROLLMENT Below is a table showing the number of students enrolled at Happy Days Preschool in the given years.
Year 2002 2004 2006 2008 2010
Students 130 168 184 201 234
a. Find an equation for the median-fit line.
b. Estimate how many students were enrolled in 2007.
Study Guide and Intervention (continued)
Regression and Median-Fit Lines
Example
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Chapter 4 39 Glencoe Algebra 1
Write an equation of the regression line for the data in each table below. Then find the correlation coefficient.
1. SOCCER The table shows the number of goals a soccer team scored each season since 2005.
Year 2005 2006 2007 2008 2009 2010
Goals Scored 42 48 46 50 52 48
2. PHYSICAL FITNESS The table shows the percentage of seventh grade students in public school who met all six of California’s physical fitness standards each year since 2002.
Year 2002 2003 2004 2005 2006
Percentage 24.0% 36.4% 38.0% 40.8% 37.5%
Source: California Department of Education
3. TAXES The table shows the estimated sales tax revenues, in billions of dollars, for Massachusetts each year since 2004.
Year 2004 2005 2006 2007 2008
Tax Revenue 3.75 3.89 4.00 4.17 4.47
Source: Beacon Hill Institute
4. PURCHASING The SureSave supermarket chain closely monitors how many diapers are sold each year so that they can reasonably predict how many diapers will be sold in the following year.
Year 2006 2007 2008 2009 2010
Diapers Sold 60,200 65,000 66,300 65,200 70,600
a. Find an equation for the median-fit line.
b. How many diapers should SureSave anticipate selling in 2011?
5. FARMING Some crops, such as barley, are very sensitive to how acidic the soil is. To determine the ideal level of acidity, a farmer measured how many bushels of barley he harvests in different fields with varying acidity levels.
Soil Acidity (pH) 5.7 6.2 6.6 6.8 7.1
Bushels Harvested 3 20 48 61 73
a. Find an equation for the regression line.
b. According to the equation, how many bushels would the farmer harvest if the soil had a pH of 10?
c. Is this a reasonable prediction? Explain.
Skills PracticeRegression and Median-Fit Lines
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Chapter 4 40 Glencoe Algebra 1
Write an equation of the regression line for the data in each table below. Then find the correlation coefficient.
1. TURTLES The table shows the number of turtles hatched at a zoo each year since 2006.
Year 2006 2007 2008 2009 2010
Turtles Hatched 21 17 16 16 14
2. SCHOOL LUNCHES The table shows the percentage of students receiving free or reduced price school lunches at a certain school each year since 2006.
Year 2006 2007 2008 2009 2010
Percentage 14.4% 15.8% 18.3% 18.6% 20.9%
Source: KidsData
3. SPORTS Below is a table showing the number of students signed up to play lacrosse after school in each age group.
Age 13 14 15 16 17
Lacrosse Players 17 14 6 9 12
4. LANGUAGE The State of California keeps track of how many millions of students are learning English as a second language each year.
Year 2003 2004 2005 2006 2007
English Learners 1.600 1.599 1.592 1.570 1.569
Source: California Department of Education
a. Find an equation for the median-fit line.
b. Predict the number of students who were learning English in California in 2001.
c. Predict the number of students who were learning English in California in 2010.
5. POPULATION Detroit, Michigan, like a number of large cities, is losing population every year. Below is a table showing the population of Detroit each decade.
Year 1960 1970 1980 1990 2000
Population (millions) 1.67 1.51 1.20 1.03 0.95
Source: U.S. Census Bureau
a. Find an equation for the regression line.
b. Find the correlation coefficient and explain the meaning of its sign.
c. Estimate the population of Detroit in 2008.
PracticeRegression and Median-Fit Lines
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Chapter 4 41 Glencoe Algebra 1
Word Problem PracticeRegression and Median-Fit Lines
1. FOOTBALL Rutgers University running back Ray Rice ran for 1732 total yards in the 2007 regular season. The table below shows his cumulative total number of yards ran after select games.
Game
Number1 3 6 9 12
Cumulative
Yards184 431 818 1257 1732
Source: Rutgers University Athletics
Use a calculator to find an equation for the regression line showing the total yards y scored after x games. What is the real-world meaning of the value returned for a?
2. GOLD Ounces of gold are traded by large investment banks in commodity exchanges much the same way that shares of stock are traded. The table below shows the cost of a single ounce of gold on the last day of trading in given years.
Year 2002 2003 2004 2005 2006
Price $346.70 $414.80 $438.10 $517.20 $636.30
Source: Global Financial Data
Use a calculator to find an equation for the regression line. Then predict the price of an ounce of gold on the last day of trading in 2009. Is this a reasonable prediction? Explain.
3. GOLF SCORES Emmanuel is practicing golf as part of his school’s golf team. Each week he plays a full round of golf and records his total score. His scorecard after five weeks is below.
Week 1 2 3 4 5
Golf Score 112 107 108 104 98
Use a calculator to find an equation for the median-fit line. Then estimate how many games Emmanuel will have to play to get a score of 86.
4. STUDENT ELECTIONS The vote totals for five of the candidates participating in Montvale High School’s student council elections and the number of hours each candidate spent campaigning are shown in the table below.
Hours
Campaigning1 3 4 6 8
Votes Received 9 22 24 46 78
a. Use a calculator to find an equation for the median-fit line.
b. Plot the data points and draw the median-fit line on the graph below.
Vote
s Re
ceiv
ed
20
30
10
0
40
50
60
70
80
Campaign Time (h)321 5 74 6 8 x
y
c. Suppose a sixth candidate spends 7 hours campaigning. Estimate how many votes that candidate could expect to receive.
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Chapter 4 42 Glencoe Algebra 1
For some sets of data, a linear equation in the form y = ax + b does not adequately describe the relationship between data points. The “QuadReg” function on a graphing calculator will output an equation in the form y = ax2 + bx + c. The value of R2, the coefficient of determination tells you how closely the parabola fits the data.
The table shows the population of Atlanta in various years.
Year 1970 1980 1990 2000 2005 2007
Population 497,000 425,000 394,017 416,474 470,688 498,109
Source: U.S. Census Bureau
a. Find the equation of a quadratic-regression parabola for the data.
Running a linear regression on the data provides an r value of 0.03, which indicates a poor fit. The data appears to be a good candidate for a quadratic regression.
Step 1 Enter the data by pressing STAT and selecting the Edit option. Enter the years since 1970 as your x-values (L1) and enter the population figures as your y-values (L2).
Step 2 Perform the quadratic regression by pressing STAT and selecting the CALC option. Scroll down to QuadReg and press ENTER .
Step 3 Write the equation of the best-fit parabola by rounding the a, b, and c values on the screen.The equation for the best-fit parabola is y = 302.8x2 – 11,480x + 501,227.
b. Find the coefficient of determination.
The coefficient of determination for the parabola is R2 = 0.969, which indicates a good fit.
c. Use the quadratic-regression parabola to predict the population in 2010.
Graph the best-fit parabola. Then use the TRACE feature and the arrow keys until you find a point where x = 40.When x ≈ 40, y ≈ 525,000. The estimated population will be 525,000.
Exercises
1. The table below shows the average high temperature in Crystal River, Florida in various months.
Month Jan (1) Mar (3) May (5) Jul (7) Sep (9) Nov (11)
Avg. High (°F) 68° 76° 87° 91° 88° 76°
Source: Country Studies
a. Find the equation of the best-fit parabola.
b. Find the coefficient of determination.
c. Use the quadratic-regression parabola to predict the average high temperature in April (4th month).
EnrichmentQuadratic Regression Parabolas
Example
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Chapter 4 43 Glencoe Algebra 1
Inverse Relations An inverse relation is the set of ordered pairs obtained by exchanging the x-coordinates with the y-coordinates of each ordered pair. The domain of a relation becomes the range of its inverse, and the range of the relation becomes the domain of its inverse.
Find and graph the inverse of the relation represented by line a.The graph of the relation passes through (–2, –10), (–1, –7), (0, –4), (1, –1), (2, 2), (3, 5), and (4, 8).
To find the inverse, exchange the coordinates of the ordered pairs.
The graph of the inverse passes through the points (–10, –2), (–7, –1), (–4, 0), (–1, 1), (2, 2), (5, 3), and (8, 4). Graph these points and then draw the line that passes through them.
ExercisesFind the inverse of each relation.
1. {(4, 7), (6, 2), (9, –1), (11, 3)} 2. {(–5, –9), (–4, –6), (–2, –4), (0, –3)}
3. x y
–8 –15
–2 –11
1 –8
5 1
11 8
4. x y
–8 3
–2 9
2 13
6 18
8 19
5. x y
–6 14
–5 11
–4 8
–3 5
–2 2
Graph the inverse of each relation.
6. y
xO
8
4
−4−8 4 8
−4
−8
7. y
xO
8
4
−4−8 4 8
−4
−8
8. y
xO
8
4
−4−8 4 8
−4
−8
Study GuideInverse Linear Functions
Example
y
xO
8
4
−4−8 4 8
−4
−8
(−10, −2)
(−4, 0) (2, 2)
(8, 4)
a
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Chapter 4 44 Glencoe Algebra 1
Study Guide (continued)
Inverse Linear Functions
Inverse Functions A linear relation that is described by a function has an inverse function that can generate ordered pairs of the inverse relation. The inverse of the linear function f (x) can be written as f -1 (x) and is read f of x inverse or the inverse of f of x.
Find the inverse of f (x) = 3 −
4 x + 6.
Step 1 f (x) = 3 −
4 x + 6 Original equation
y = 3 −
4 x + 6 Replace f (x) with y.
Step 2 x = 3 −
4 y + 6 Interchange y and x.
Step 3 x - 6 = 3 −
4 y Subtract 6 from each side.
4 −
3 (x - 6) = y Multiply each side by 4 −
3 .
Step 4 4 −
3 (x - 6) = f -1 (x) Replace y with f -1 (x).
The inverse of f (x) = 3 −
4 x + 6 is f -1 (x) = 4 −
3 (x - 6) or f -1 (x) = 4 −
3 x - 8.
ExercisesFind the inverse of each function.
1. f (x) = 4x - 3 2. f (x) = -3x + 7 3. f (x) = 3 −
2 x - 8
4. f (x) = 16 - 1 −
3 x 5. f (x) = 3(x - 5) 6. f (x) = -15 - 2 −
5 x
7. TOOLS Jimmy rents a chainsaw from the department store to work on his yard. The total cost C(x) in dollars is given by C(x) = 9.99 + 3.00x, where x is the number of days he rents the chainsaw.
a. Find the inverse function C -1 (x).
b. What do x and C -1 (x) represent in the context of the inverse function?
c. How many days did Jimmy rent the chainsaw if the total cost was $27.99?
Example
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Chapter 4 45 Glencoe Algebra 1
Find the inverse of each relation.
1. x y
–9 –1
–7 –4
–5 –7
–3 –10
–1 –13
2. x y
1 8
2 6
3 4
4 2
5 0
3. x y
–4 –2
–2 –1
0 1
2 0
4 2
4. {(-3, 2), (-1, 8), (1, 14), (3, 20)} 5. {(5, -3), (2, -9), (-1, -15), (-4, -21)}
6. {(4, 6), (3, 1), (2, -4), (1, -9)} 7. {(-1, 16), (-2, 12), (-3, 8), (-4, 4)}
Graph the inverse of each function.
8. y
xO
8
4
−4−8 4 8
−4
−8
9. y
xO
8
4
−4−8 4 8
−4
−8
10. y
xO
8
4
−4−8 4 8
−4
−8
Find the inverse of each function.
11. f (x) = 8x - 5 12. f (x) = 6(x + 7) 13. f (x) = 3 −
4 x + 9
14. f (x) = -16 + 2 −
5 x 15. f (x) = 3x + 5 −
4 16. f (x) = -4x + 1 −
5
17. LEMONADE Chrissy spent $5.00 on supplies and lemonade powder for her lemonade stand. She charges $0.50 per glass.
a. Write a function P(x) to represent her profit per glass sold.
b. Find the inverse function, P -1 (x).
c. What do x and P -1 (x) represent in the context of the inverse function?
d. How many glasses must Chrissy sell in order to make a $3 profit?
Skills PracticeInverse Linear Functions
4-7
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Chapter 4 46 Glencoe Algebra 1
Find the inverse of each relation.
1. {(-2, 1), (-5, 0), (-8, -1), (-11, 2)} 2. {(3, 5), (4, 8), (5, 11), (6, 14)}
3. {(5, 11), (1, 6), (-3, 1), (-7, -4)} 4. {(0, 3), (2, 3), (4, 3), (6, 3)}
Graph the inverse of each function.
5. y
xO
8
4
−4−8 4 8
−4
−8
6. y
xO
8
4
−4−8 4 8
−4
−8
7. y
xO
8
4
−4−8 4 8
−4
−8
Find the inverse of each function.
8. f (x) = 6 −
5 x - 3 9. f (x) = 4x + 2 −
3 10. f (x) = 3x - 1 −
6
11. f (x) = 3(3x + 4) 12. f (x) = -5(-x - 6) 13. f (x) = 2x - 3 −
7
Write the inverse of each equation in f -1 (x) notation.
13. 4x + 6y = 24 14. -3y + 5x = 18 15. x + 5y = 12
16. 5x + 8y = 40 17. -4y - 3x = 15 + 2y 18. 2x - 3 = 4x + 5y
19. CHARITY Jenny is running in a charity event. One donor is paying an initial amount of $20.00 plus an extra $5.00 for every mile that Jenny runs.
a. Write a function D(x) for the total donation for x miles run.
b. Find the inverse function, D -1 (x).
c. What do x and D -1 (x) represent in the context of the inverse function?
PracticeInverse Linear Functions
4-7
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Chapter 4 47 Glencoe Algebra 1
Word Problem PracticeInverse Linear Functions
1. BUSINESS Alisha started a baking business. She spent $36 initially on supplies and can make 5 dozen brownies at a cost of $12. She charges her customers $10 per dozen brownies.
a. Write a function C(x) to represent Alisha’s total cost per dozen brownies.
b. Write a function E(x) to represent Alisha’s earnings per dozen brownies sold.
c. Find P (x) = E(x) - C(x). What does P (x) represent?
d. Find C -1 (x), E -1 (x), and P -1 (x).
e. How many dozen brownies does Alisha need to sell in order to make a profit?
2. GEOMETRY The area of the base of a cylindrical water tank is 66 square feet. The volume of water in the tank is dependent on the height of the water hand is represented by the function V(h) = 66h. Find V -1 (h). What will the height of the water be when the volume reaches 2310 cubic feet?
3. SERVICE A technician is working on a furnace. He is paid $150 per visit plus $70 for every hour he works on the furnace.
a. Write a function C(x) to represent the total charge for every hour of work.
b. Find the inverse function, C -1 (x).
c. How long did the technician work on the furnace if the total charge was $640?
4. FLOORING Kara is having baseboard installed in her basement. The total cost C(x) in dollars is given by C(x) = 125 + 16x, where x is the number of pieces of wood required for the installation.
a. Find the inverse function C -1 (x).
b. If the total cost was $269 and each piece of wood was 12 feet long, how many total feet of wood were used?
5. BOWLING Libby’s family went bowling during a holiday special. The special cost $40 for pizza, bowling shoes, and unlimited drinks. Each game cost $2. How many games did Libby bowl if the total cost was $112 and the six family members bowled an equal number of games?
4-7
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Chapter 4 48 Glencoe Algebra 1
In a function, there is exactly one output for every input. In other words, every element in the domain pairs with exactly one element in the range. When a function is one-to-one, each element of the domain pairs with exactly one unique element in the range. When a function is onto, each element of the range corresponds to an element in the domain.
If a function is both one-to-one and onto, then the inverse is also a function.
Determine whether each relation is a function. If it is a function, determine if it is one-to-one, onto, both, or neither.
1. 1116
-34
369
12
2. 12345
-3-2
045
3. 369
1215
1050
-5
4. 427
116
1-2-4
7
5. 26
13
23468
6. 31
-910
24
111719
Determine whether the inverse of each function is also a function.
7. y
xO
8
4
−4−8 4 8
−4
−8
8. y
xO
8
4
−4−8 4 8
−4
−8
9. y
xO
8
4
−4−8 4 8
−4
−8
EnrichmentOne-to-One and Onto Functions
26912
-13589
one–to–one
-3-2-1
26
35
10
onto
579
10
-6-11-15-19
both
4-7
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PDF Pass
Chapter 4 49 Glencoe Algebra 1
Read each question. Then fill in the correct answer.
1. A B C D
2. F G H J
3. A B C D
4. F G H J
5. A B C D
6. F G H J
Multiple Choice
Student Recording SheetUse this recording sheet with pages 280–281 of the Student Edition.
Short Response/Gridded Response
Record your answer in the blank.
For gridded response questions, also enter your answer in the grid by writing each number or symbol in a box. Then fill in the corresponding circle for that number or symbol.
7.
8. (grid in)
9.
10a.
10b.
11a.
11b.
11c.
8.
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
. . . . .
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
Extended Response
Record your answers for Question 12 on the back of this paper.
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Chapter 4 50 Glencoe Algebra 1
4 Rubric for Scoring Extended Response Test
General Scoring Guidelines
• If a student gives only a correct numerical answer to a problem but does not show how he or she arrived at the answer, the student will be awarded only 1 credit. All extended response questions require the student to show work.
• A fully correct answer for a multiple-part question requires correct responses for all parts of the question. For example, if a question has three parts, the correct response to one or two parts of the question that required work to be shown is not considered a fully correct response.
• Students who use trial and error to solve a problem must show their method. Merely showing that the answer checks or is correct is not considered a complete response for full credit.
Exercise 12 Rubric
Score Specifi c Criteria
4 Student explain that the slopes of the lines must be compared. If two lines have the same slope, they are parallel. If their slopes are opposite reciprocals, they are perpendicular.
3 A generally correct solution, but may contain minor flaws in reasoning or computation.
2 A partially correct interpretation and/or solution to the problem.
1 A correct solution with no evidence or explanation.
0 An incorrect solution indicating no mathematical understanding of the concept or task, or no solution is given.
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Chapter 4 51 Glencoe Algebra 1
4
4
SCORE
For Questions 1 and 2, write an equation in slope-intercept form for each situation.
1. slope: 1 −
4 , y-intercept: -5
2. line passing through (9, 2) and (-2, 6)
3. Graph 4x + 3y = 12.
4. Write a linear equation in slope-intercept form to model a tree 4 feet tall that grows 3 inches per year.
5. MULTIPLE CHOICE The table of ordered pairsshows the coordinates of the two points onthe graph of a function. Which equationdescribes the function?A y = -2x + 1 C y = - 1 −
2 x + 1
B y = 1 −
2 x - 1 D y = - 1 −
2 x - 1
Chapter 4 Quiz 2 (Lessons 4-3 and 4-4)
Chapter 4 Quiz 1 (Lessons 4-1 and 4-2)
x y
-2 2
4 -1
1. Write an equation in point-slope form for a line that
passes through (3, 6) with a slope of -
1 −
3 .
2. Write y - 9 = -(x + 2) in slope-intercept form.
3. Write an equation in point-slope form for a horizontal line that passes through (-4, -1).
4. Write an equation in slope-intercept form for the line that passes through (5, 3) and is parallel to x + 3y = 6.
5. MULTIPLE CHOICE Line DE contains the points D (-1, -4) and E (3, 3). Line FG contains the point F (-3, 3). Which set of coordinates for point G makes the two lines perpendicular?
A (1, 7) C (1, 4)
B (1, 10) D (4, -1)
SCORE
1.
2.
3. y
xO
4.
5.
1.
2.
3.
4.
5.
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Chapter 4 52 Glencoe Algebra 1
4
4
SCORE Chapter 4 Quiz 3(Lessons 4-5 and 4-6)
1. Find the inverse of {(1, 3), (4, -1), (7, -5), (10, -9)}.
2. Graph the inverse of the functiongraphed at the right.
Find the inverse of each function.
3. f (x) = 4x + 6 4. f (x) = 3 −
4 x - 8
5. MULTIPLE CHOICE Write the inverse of 3x + 4y = 12 in f -1 (x) notation.
A f -1 (x) = 12 - 4x −
3 B f -1 (x) = 12 - 3x −
4
C f -1 (x) = 12 - 3x D f -1 (x) = 12 - 4y
−
3
Chapter 4 Quiz 4 (Lesson 4-7)
For Questions 1–5, use the table.
Age (years) 26 27 28 29 30
Median Income
($1000)16.8 19.1 23.3 25.8 33.9
1. Make a scatter plot relating age to median income. Then draw a fit line for the scatter plot.
2. Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning.
3. Write an equation of the best-fit line for the data in the table.
4. Use the line of fit to predict the median income for 32-year olds.
5. MULTIPLE CHOICE What is the correlation coefficient for the best-fit line?
A 4.09 B –90.74 C 0.943 D 0.971
SCORE
1.
2.
3.
4.
5.
Age (years)
Med
ian
Inco
me
($10
00)
16
19
22
25
28
31
260 27 28 29 30
y
xO
8
4
−4−8 4 8
−4
−8
1.
2.
3.
4.
5.
y
xO
8
4
−4−8 4 8
−4
−8
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Chapter 4 53 Glencoe Algebra 1
4 SCORE
Write the letter for the correct answer in the blank at the right of each question.
1. Which is the slope-intercept form of an equation for the line containing (0, -3) with slope -1?
A y = -x - 3 B y = -3x - 1 C y = x + 3 D x = -3y - 1
2. Write an equation in slope-intercept form of the line with a slope of - 3 −
4
and y-intercept of – 5.
F y = 5x - 3 −
4 G 3x + 4y = 20 H y = -
3 −
4 x - 5 J y = -
3 −
4 x + 5
3. Write an equation of the line that passes through (-2, 8) and (-4, -4).
A y = 2x + 12 B y = 6x + 20 C y = -6x - 4 D y = 1 −
6 x + 25 −
3
4. Write y - 3 = 2 −
3 (x - 2) in standard form.
F 2x - 3y = 5 G y = 2 −
3 x + 5 −
3 H -2x + 3y = -5 J 2x - 3y = -5
5. Write y - 1 = 2 (x - 3 −
2 ) in slope-intercept form.
A 2x - y = 2 B 1 −
2 y + 1 −
2 = x C y = 2x -
1 −
2 D y = 2x - 2
6. A cell phone company charges $42 per month of service. The cost of a new cell phone, plus 8 months of service, is $415.99. How much does it cost to buy a new cell phone and 3 months of service?
F $79.99 G $126.00 H $205.99 J $289.99
Part IIFor Questions 7–10, use the following information.
Nikko needs to get his air-conditioner fixed. The technician will charge Nikko a flat fee of $50 plus an additional $20 for each hour of work.
7. Write an equation to represent Nikko’s total cost to repair his air-conditioner. Use t for total cost and h for hours.
8. Graph this equation.
9. How much will it cost Nikko if the technician has to spend 4 hours working on the air-conditioner?
10. How many hours must the technician work for it to cost Nikko $180?
1.
2.
3.
4.
5.
6.
Ass
essm
ent
Chapter 4 Mid-Chapter Test (Lessons 4-1 through 4-3)
Part I
7.
8.
9.
10.
1
Hours2 3 4 5 6 7 8 9 10
20406080
100
Tota
l Cos
t ($)
120140160180200
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Chapter 4 54 Glencoe Algebra 1
4 SCORE
Choose from the terms above to complete each sentence.
1. If two lines have slopes that are negative reciprocals of each
other, then they are .
2. A(n) is the set of ordered pairs obtained by exchanging the x-coordinates with the y-coordinates of each ordered pair of a relation or function.
3. A graph of data points is sometimes called a
.
4. If two lines have slopes that are the same, then they are
.
5. The number that describes how closely a best-fit line models a
set of data is called the .
6. The leftmost data point in a set is (3, 27) and the rightmost point is (12, 13). If you use a linear prediction equation to findthe corresponding y-value for x = 10, you are using a method
called .
7. The leftmost data point in a set is (1997, 24) and the rightmostpoint is (2011, 38). If you use a linear prediction equation to find the corresponding y-value for x = 2012, you are using a
method called .
8. The equation y = -3x + 12 is written in form.
9. The equation y + 6 = 2(x - 4) is written in form.
Define each term in your own words.
10. line of fit
11. linear extrapolation
Chapter 4 Vocabulary Test
best-fi t line
bivariate data
correlation coefficient
inverse function
inverse relation
linear extrapolation
linear interpolation
linear regression
median-fi t line
line of fi t
parallel lines
perpendicular lines
point-slope form
rate of change
scatter plot
slope-intercept form
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
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Chapter 4 55 Glencoe Algebra 1
4 SCORE Chapter 4 Test, Form 1
Write the letter for the correct answer in the blank at the right of each question.
For Questions 1–5, find the equation in slope-intercept form that describes each line. 1. a line with slope -2 and y-intercept 4 A y = -2x B y = 4x - 2 C y = -2x + 4 D y = 2x - 4
2. a line through (2, 4) with slope 0 F y = 2 G x = 2 H y = 4 J x = 4
3. a line through (4, 2) with slope 1 −
2
A y = - 1 −
2 x B y = 1 −
2 x - 4 C y = 2x - 10 D y = 1 −
2 x
4. a line through (-1, 1) and (2, 3) F y = 2 −
3 x + 5 −
3 G y = -
2 −
3 x + 5 −
3 H y = 2 −
3 x - 5 −
3 J y = -
2 −
3 x - 5 −
3
5. the line graphed at the right
A y = 2 −
3 x - 1 C y = 2 −
3 x + 3 −
2
B y = 3 −
2 x - 1 D y = 3 −
2 x + 3 −
2
6. If 5 deli sandwiches cost $29.75, how much will 8 sandwiches cost? F $37.75 G $29.75 H $47.60 J $0.16
7. What is the standard form of y - 8 = 2(x + 3)? A 2x + y = 14 B y = 2x + 14 C 2x - y = -14 D y - 2x = 11
8. Which is the graph of 3x - 4y = 6 ? F y
xO
G y
xO
H y
xO
J y
xO
9. Which is the point-slope form of an equation for the line that passes through (0, -5) with slope 2?
A y = 2x - 5 B y + 5 = 2x C y - 5 = x - 2 D y = 2(x + 5)
10. What is the slope-intercept form of y + 6 = 2(x + 2)? F y = 2x - 6 G y = 2x - 2 H y = 2x + 6 J 2x - y = 6
11. When are two lines parallel? A when the slopes are opposite B when the slopes are equal C when the slopes are positive D when the product of the slopes is -1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
y
xO
(3, 1)
(0, -1)
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Chapter 4 56 Glencoe Algebra 1
4 Chapter 4 Test, Form 1 (continued)
12. Find the slope-intercept form of an equation for the line that passes through (-1, 2) and is parallel to y = 2x - 3.
F y = 2x + 4 G y = 0.5x + 4 H y = 2x + 3 J y = -0.5x - 4
13. Find the slope-intercept form of an equation of the line perpendicular to the graph of x - 3y = 5 and passing through (0, 6).
A y = 1 −
3 x - 2 B y = -3x + 6 C y = 1 −
3 x + 2 D y = 3x - 6
For Questions 14 and 15, use the scatter plot shown.
14. How would you describe the relationship between the x- and y-values in the scatter plot?
F strong negative correlation G weak negative correlation H weak positive correlation J strong positive correlation
15. Based on the data in the scatter plot, what would you expect the y-value to be for x = 2020?
A greater than 80 C between 65 and 50 B between 80 and 65 D less than 50
16. Which equation has a slope of 2 and a y-intercept of -5? F y = -5x + 2 G y = 5x + 2 H y = 2x + 5 J y = 2x - 5
17. Which correlation coefficient corresponds to the best-fit line that most closely models its set of data?
A 0.84 B 0.13 C -0.87 D -0.15
18. The table below shows Mia’s bowling score each week she participated in a bowling league.
Week 1 2 3 4 5 6
Score 122 131 130 133 145 139
Use the median-fit line to estimate Mia’s score for week 16. F 173 G 180 H 182 J 257
19. If f(x) = 6x + 3, find f -1 (x).
A f -1 (x) = 6x - 3 B f -1 (x) = x - 6 −
3 C f -1 (x) = x - 3 −
6 D f -1 (x) = -3 - 6x
20. If f(x) = 4(3x - 5), find f -1 (x).
F f -1 (x) = x + 5 −
12 G f -1 (x) = x + 20 −
12 H f -1 (x) = x - 20 −
12 J f -1 (x) = x + 5 −
4
Bonus Find the value of r in (4, r), (r, 2) so that the slope of the
line containing them is - 5 −
3 .
0
50
60
70
80
90
'90 '95 '00 '05 '10
B:
12.
13.
14.
15.
16.
17.
18.
19.
20.
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NAME DATE PERIOD
PDF Pass
Chapter 4 57 Glencoe Algebra 1
4 SCORE
Ass
essm
entWrite the letter for the correct answer in the blank at the right of each question.
1. What is the slope-intercept form of the equation of a line with a slope of 5 and a y-intercept of -8?
A y = -8x + 5 B y = 8x - 5 C 5x - y = - 8 D y = 5x - 8
2. Which equation is graphed at the right? F 2y - x =10 H 2x - y = 5 G 2x + y = -5 J 2y + x = -5
3. Which is an equation of the line that passes through (2, -5) and (6, 3)?
A y = 1 −
2 x - 6 C y = 2x + 12
B y = 1 −
2 x D y = 2x - 9
4. What is an equation of the line through (0, -3) with slope 2 −
5 ?
F -5x + 2y = 15 H 2x - 5y = 15 G -5x - 2y = -15 J -2x + 5y = 15
5. Which is an equation of the line with slope -3 and a y-intercept of 5? A y = -3(x + 5) B y - 5 = -3x C -3x + y = 5 D y = 5x - 3
6. What is the equation of the line through (-2, -3) with a slope of 0?
F x = -2 G y = -3 H -2x - 3y = 0 J -3x + 2y = 0
7. Find the slope-intercept form of the equation of the line that passes through (-5, 3) and is parallel to 12x - 3y = 10.
A y = -4x - 17 B y = 4x - 13 C y = - 4x + 13 D y = 4x + 23
8. If line q has a slope of - 3 −
8 , what is the slope of any line perpendicular to q?
F -
3 −
8 G 3 −
8 H 8 −
3 J -
8 −
3
9. A line of fit might be defined as A a line that connects all the data points. B a line that might best estimate the data and be used for predicting values. C a vertical line halfway through the data. D a line that has a slope greater than 1.
10. A scatter plot of data comparing the number of years since Holbrook High School introduced a math club and the number of students participating contains the ordered pairs (3, 19) and (8, 42). Which is the slope-intercept form of an equation for the line of fit?
F y = 4.6x + 5.2 G y = 3x + 1 H y = 5.2x + 4.6 J y = 0.22x - 1.13
11. Use the equation from Question 10 to estimate the number of students who will be in the math club during the 15th year.
A 53 B 61 C 65 D 74
Chapter 4 Test, Form 2A
y
xO
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
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NAME DATE PERIOD
PDF Pass
Chapter 4 58 Glencoe Algebra 1
4
For Questions 12–14, use the scatter plot shown.
12. Which data are shown by the scatter plot? F (1995, 5.5), (1997, 6.1), (2004, 7.6) G (1995, 5.5), (2000, 6.1), (2004, 7.6) H (1995, 5.5), (2000, 6.6), (2005, 8.0) J (1995, 5.5), (1997, 6.6), (2005, 8.0)
13. Which is true about the data? A The slope of a best-fit line would be negative. B There is a positive correlation. C There is no correlation. D There is a negative correlation.
14. Based on the data in the scatter plot, what would you expect the y-value to be for x = 2010?
F between 7 and 8 H between 5 and 7 G higher than 8 J impossible to tell
15. To calculate the charge for a load of bricks, including delivery, the Redstone Brick Co. uses the equation C = 0.42b + 25, where C is the charge and b is the number of bricks. What is the delivery fee per load?
A $42 C $25 B $67 D It depends on the number of bricks
For Questions 16 and 17, use the table shown.
Shots on Goal 22 25 28 29 33
Points Scored 5 7 7 9 8
16. Find the slope of the best-fit line. F -0.561 G 0.283 H 0.631 J 0.794
17. Estimate how many points would be scored if 80 shots were taken on the goal using the best-fit line.
A 18 B 19 C 22 D 24
18. Find the inverse of {(4, -1), (3, -2), (6, 9), (8, 5)}. F {(8, 5), (6, 9), (3, -2), (4, -1)} H {(-1, 4), (-2, 3), (9, 6), (5, 8)} G {(-4, 1), (-3, 2), (-6, -9), (-8, -5)} J {(-1, -2), (9, 5), (4, 3), (6, 8)}
19. If f (x) = 3x - 4, find f -1 (x).
A f -1 (x) = 4x - 3 B f -1 (x) = x + 4 −
3 C f -1 (x) = x - 4 −
3 D f -1 (x) = -4 - 3x
20. If f (x) = 8(5x - 2), find f -1 (x).
F f -1 (x) = 5x + 2 −
8 G f -1 (x) = 5x - 2 −
8 H f -1 (x) = x - 16 −
40 J f -1 (x) = x + 16 −
40
Bonus What is the y-intercept of a line through (2, 7) and
perpendicular to the graph of y = -
3 −
2 x + 6?
Chapter 4 Test, Form 2A (continued)
0
5
6
7
8
'95 '00 '05 12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
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Chapter 4 59 Glencoe Algebra 1
4 SCORE
Write the letter for the correct answer in the blank at the right of each question.
1. What is the slope-intercept form of the equation of the line with a slope of 1 −
4
and y-intercept at the origin? A y = 4x B y = 1 −
4 x C y = x + 1 −
4 D y + 1 −
4 = x
2. Which equation is graphed at the right? F y - 2x = -4 H 2x + y = 4 G 2x + y = -4 J y - 4 = 2x
3. Which is an equation of the line that passes through (4, -5) and (6, -9)?
A y = 1 −
2 x - 3 B y = 1 −
2 x + 3 C y = -2x + 3 D y = 2x - 3
4. What is the standard form of the equation of the line through (6, -3) with a
slope of 2 −
3 ?
F -2x + 3y = 24 G 2x - 3y = 21 H 3x - 2y = 24 J 3x - 2y = -21
5. Which is an equation of the line with a slope of -3 that passes through (2, 4)? A y - 4 = -3(x - 2) C y + 4 = -3(x + 2) B y - 4 = -3x - 2 D y - 2 = -3(x - 4)
6. What is the equation of the line through (-2, -3) with an undefined slope? F x = -2 G y = -3 H -2x - 3y = 0 J -3x + 2y = 0
7. Find the slope-intercept form of the equation of the line that passes through (-1, 5) and is parallel to 4x + 2y = 8.
A y = -2x + 9 B y = 2x - 9 C y = 4x - 9 D y = -2x + 3
8. If line q has a slope of -2, what is the slope of any line perpendicular to q? F 2 G -2 H 1 −
2 J - 1 −
2
9. The graph of data that has a strong negative correlation has A a narrow linear pattern from lower left to upper right. B a narrow linear pattern from upper left to lower right. C a narrow horizontal pattern below the x-axis. D all negative x-values.
10. A scatter plot of data comparing the time in minutes Beverly spends studying for her math test and the score she received on the test contains the ordered pairs (45, 89) and (60, 94). Which is the slope-intercept form of an equation for the line of fit?
F 0.573x + 63.2 = y G 1 −
3 x + 74 = y
H 3x - 46 = y J - 1 −
3 x + 104 = y
11. Estimate how well Beverly would score on her next test if she spent 20 minutes studying.
A 75 B 81 C 84 D 90
Chapter 4 Test, Form 2B
O
y
x
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
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PDF Pass
Chapter 4 60 Glencoe Algebra 1
4
For Questions 12–14, use the scatter plot shown.
12. Which data are shown by the scatter plot? F (1985, 47), (1995, 31), (2001, 24) G (1985, 50), (2000, 25), (2005, 0) H (47, 1985), (31, 1995), (24, 2001) J (1991, 45), (1995, 35), (2000, 8)
13. Based on the data in the scatter plot, which statement is true?
A As x increases, y increases. B As x increases, y decreases. C There is no relationship between x and y. D There are not enough data to determine the relationship between x and y.
14. Based on the scatter plot, what would you expect the y-value to be for x = 1992? F between 40 and 45 H between 30 and 40 G higher than 45 J impossible to tell
15. A baby blue whale weighed 3 tons at birth. Ten days later, it weighed 4 tons. Assuming the same rate of growth, which equation shows the weight w when the whale is d days old?
A w = 10d + 3 B w = 10d + 4 C w = 0.1d + 3 D w = d + 10
For Questions 16 and 17, use the table shown.
Times at Bat 4 5 8 12 22
Hits 1 0 2 4 6
16. Find the correlation coefficient of the best-fit line. F -0.631 G 0.317 H 0.920 J 0.959
17. Estimate how many hits a batter would get with 72 times at bat using the best-fit line.
A 18 B 19.6 C 20 D 22
18. Find the inverse of {(2, -1), (5, -2), (6, 9), (7, 5)}. F {(7, 5), (6, 9), (5, -2), (2, -1)} H {(-1, -2), (9, 5), (2, 5), (6, 7)} G {(-2, 1), (-5, 2), (-6, -9), (-7, -5)} J {(-1, 2), (-2, 5), (9, 6), (5, 7)}
19. If f (x) = 4x + 3, find f -1 (x).
A f -1 (x) = 4x - 3 B f -1 (x) = x - 3 −
4 C f -1 (x) = x - 4 −
3 D f -1 (x) = -3 - 4x
20. If f (x) = 7(2x - 9), find f -1 (x).
F f -1 (x) = x + 9 −
7 G f -1 (x) = 2x + 9 −
7 H f -1 (x) = x + 63 −
14 J f -1 (x) = x - 63 −
14
Bonus For what value of k does kx + 7y = 10 have a slope of 3?
Chapter 4 Test, Form 2B (continued)
25
30
35
40
45
'85 '95 '05
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
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Chapter 4 61 Glencoe Algebra 1
4 SCORE
1. Write a linear equation in slope-intercept form to model the situation: A telephone company charges $28.75 per month plus $0.10 a minute for long-distance calls.
2. Write an equation in standard form of the line that passes through (7, -3) and has a y-intercept of 2.
3. Write the slope-intercept form of an equation for the line graphed at the right.
4. Graph the line with a y-intercept of 3 and slope -
3 −
4 .
5. Write an equation in slope-intercept form for the line that passes through (-1, -2) and (3, 4).
6. Write an equation in standard form for the line that has an undefined slope and passes through (-6, 4).
7. Write an equation in point-slope form for the line that has slope 1 −
3 and passes through (-2, 8).
8. Write the standard form of the equation y + 4 = -
12 −
7 (x - 1).
9. Write the slope-intercept form of the equation y - 2 = 3(x - 4).
10. Write the slope-intercept form of the equation of the line parallel to the graph of 2x + y = 5 that passes through (0, 1).
11. Write the slope-intercept form of the equation of the line
perpendicular to the graph of y = -
3 −
2 x - 7 that passes
through (3, -2).
12. A scatter plot of data showing the percentage of total Internet users who visited an online store on a given day in December includes the points (2008, 2.0) and (2010, 4.5). Write the slope-intercept form of an equation for the line of fit.
1.
2.
3.
4. y
xO
5.
6.
7.
8.
9.
10.
11.
12.
Chapter 4 Test, Form 2C
y
xO
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PDF Pass
Chapter 4 62 Glencoe Algebra 1
4
For Questions 13–15, use the data in the table.
Time Spent Studying (min) 10 20 30 40 50
Score Received (percent) 53 67 78 87 95
13. Make a scatter plot relating time spent studying to the score received.
14. Write the slope-intercept form of the equation for a line of fit for the data. Use your equation to predict a student’s score if the student spent 35 minutes studying.
15. Is it reasonable to use the equation to estimate the score received for any length of time spent studying?
For Questions 16 and 17, use the data in the table showing the number of congressional seats apportioned to California each decade.
Decade 1940s 1950s 1970s 1990s 2000s
Seats 23 30 43 52 53
Source: Office of the Clerk, U.S. House of Representatives
16. Find an equation for the median-fit line.
17. Predict the number of seats apportioned to California in the 1930s.
18. Graph the inverse of the function graphed at the right.
19. If f (x) = 5 - 4x −
15 , find f -1 (x).
20. Write the inverse of 6x + 8y = 13 in f -1 (x) notation.
Bonus In a certain lake, a 1-year-old bluegill fish is 3 inches long, while a 4-year-old bluegill fish is 6.6 inches long. Assuming the growth rate can be approximated by a linear equation, write an equation in slope-intercept form for the length � of a bluegill fish in inches after t years. Then use the equation to determine the age of a 9-inch bluegill.
Chapter 4 Test, Form 2C (continued)
13.
14.
15.
16.
17.
18. y
xO
8
4
−4−8 4 8
−4
−8
19.
20.
B:
Time Spent Studying(minutes)
Sco
re R
ecei
ved
(per
cen
t)
0
60
70
80
90
100
10 20 30 40 50
y
xO
8
4
−4−8 4 8
−4
−8
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Chapter 4 63 Glencoe Algebra 1
4 SCORE
1. Write a linear equation in slope-intercept form to model the situation: An Internet company charges $4.95 per month plus $2.50 for each hour of use.
2. Write an equation in standard form of the line that passes through (3, 1) and has a y-intercept of -2.
3. Write the slope-intercept form of an equation for the line graphed at the right.
4. Graph the line with y-intercept 2 and slope -
1 −
2 .
5. Write an equation in slope-intercept form for the line that passes through (5, 4) and (6, -1).
6. Write an equation in standard form for the line that has an undefined slope and passes through (5, -3).
7. Write an equation in point-slope form for the line that has
a slope of 4 −
3 and passes through (3, 0).
8. Write the standard form of the equation y - 3 = - 2 −
3 (x + 5).
9. Write the slope-intercept form of the equation
y - 1 = 3 −
4 (x - 3).
10. Write the slope-intercept form of the equation of the line parallel to the graph of 9x + 3y = 6 that passes through (5, 3).
11. Write the slope-intercept form of the equation of the line perpendicular to the graph of 4x - y = 12 that passes through (8, 2).
12. A scatter plot of data showing the percentage of total Internet users who visit a video sharing Web site on a given day in December includes the points (2010, 17.0) and (2008, 0.3). Write the slope-intercept form of an equation for the line of fit.
Chapter 4 Test, Form 2D
y
xO
1.
2.
3.
4. y
xO
5.
6.
7.
8.
9.
10.
11.
12.
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Chapter 4 64 Glencoe Algebra 1
4
For Questions 13–15, use the data that shows age and percent of budget spent on entertainment in the table.
Age 30 40 50 60 70 80
Percent Spent on Entertainment 6.1 6.0 5.4 5.0 4.7 3.4
13. Make a scatter plot relating the age to the percent of the person’s budget spent on entertainment.
14. Write the slope-intercept form of the equation for a line of fit for the data. Use your equation to predict the percent of a 65-year-old person’s budget.
15. Is it reasonable to use the equation to estimate the entertainment spending for any age?
For Questions 16 and 17, use the data in the table showing the number of congressional seats apportioned to Texas each decade.
Decade 1960s 1970s 1980s 1990s 2000s
Seats 23 24 27 30 32
Source: Office of the Clerk, U.S. House of Representatives
16. Find an equation for the median-fit line.
17. Predict the number of seats that will be apportioned to Texas in the 2010s.
18. Graph the inverse of the graph shown.
19. If f (x) = 8 - 3x −
18 , find f -1 (x).
20. Write the inverse of 5x - 17 = 11 + 3y in f -1 (x) notation.
Bonus Write an equation in slope-intercept form of the line with y-intercept -6 and parallel to a line perpendicular to 5x + 6y - 13 = 0.
Chapter 4 Test, Form 2D (continued)
13.
14.
15.
16.
17.
18. y
xO
8
4
−4−8 4 8
−4
−8
19.
20.
B:
Age
Perc
ent
Spen
t o
nEn
tert
ain
men
t
3
4
5
6
300 40 50 60 70 80
y
xO
8
4
−4−8 4 8
−4
−8
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Chapter 4 65 Glencoe Algebra 1
4 SCORE
For Questions 1–4, write an equation in slope-intercept form of the line satisfying the given conditions.
1. has y-intercept -8 and slope 3
2. has slope 5 −
2 and passes through (4, -1)
3. passes through (-3, 7) and (2, 4)
4. is horizontal and passes through (-4, 6)
5. Write the point-slope form of an equation of the line that has a slope of - 3 −
5 and passes through (2, 1).
6. Write an equation in standard form of the line that passes through (2, -3) and (-3, 7).
7. Graph a line that has an x-intercept of 5 and a slope of - 3 −
5 .
8. Write y + 4 = - 2 −
3 (x - 9) in standard form.
9. Write the point-slope form of the equation for the line that has x-intercept -3 and y-intercept -2.
For Questions 10–13, write an equation in slope-intercept form of the line satisfying the given conditions.
10. is parallel to the y-axis and has an x-intercept of 3
11. is perpendicular to 4y = 3x - 8 and passes through (-12, 7)
12. is parallel to 3x - 5y = 7 and passes through (0, -6)
13. is perpendicular to the y-axis and passes through (-2, 5)
Chapter 4 Test, Form 3
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
y
xO
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Chapter 4 66 Glencoe Algebra 1
4
For Questions 14–16, use the data in the table.
14. Make a scatter plot relating the verbal scores and the math scores.
State Graduation Scores
Year Verbal Score Math Score
1975 460 488
1985 424 466
1995 410 463
2005 420 460
15. Does the scatter plot in Question 14 show a positive, a negative, or no correlation? What does that relationship represent?
16. Write the equation for a line of fit. Predict the corresponding math score for a verbal score of 445.
17. The data in the table show the number of congressional seats apportioned to the state of New York each decade.
Decade 1940s 1960s 1980s 2000s
Seats 45 41 34 29
Source: Office of the Clerk, U.S. House of Representatives
Find an equation for the median-fit line and predict the number of seats that will be apportioned to New York in the 2020s.
18. Graph the inverse of the function graphed at the right.
19. If f (x) = 3(4 - 5x) −
8 , find f -1 (x).
20. Write the inverse of 4x - 13 = 2x + 3y in f -1 (x) notation.
Bonus The area of a circle varies directly as the square of the radius. If the radius is tripled, by what factor will the area increase?
Chapter 4 Test, Form 3 (continued)
14.
15.
16.
17.
18. y
xO
8
4
−4−8 4 8
−4
−8
19.
20.
B:
Verbal Score
Mat
h S
core
450
460
470
480
490
500
4000 440 480
y
xO
8
4
−4−8 4 8
−4
−8
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Chapter 4 67 Glencoe Algebra 1
4 SCORE
Demonstrate your knowledge by giving a clear, concise solution to each problem. Be sure to include all relevant drawings and justify your answers. You may show your solution in more than one way or investigate beyond the requirements of the problem.
1. You are told that a line passes through (-2, 3). a. Discuss what other information you would need to graph this
line. b. Then describe how you would use that information to graph
the line and write its equation.
2. Refer to the scatter plot at the right. a. Describe the pattern of points in the
scatter plot and the relationship between x and y.
b. Give at least two examples of real-life situations that, if graphed, would result in a correlation like the one shown in this scatter plot.
c. Add a scale and heading to each axis. Then write an equation that would model the points represented by this plot.
3. The table gives the life expectancy of a child born in the United States in a given year.
a. Make a scatter plot of the data. b. Can you use the data to claim
that the increase in life expectancy is due to improved health care? Explain your response.
c. Use the data to predict the life expectancy of a baby born in 2000. Explain how you determined your answer.
Source: National Center for Health Statistics
Chapter 4 Extended-Response Test
y
xO
Years of Life Expected at Birth
Year of Birth
Life Expectancy (years)
1920 54.1
1930 59.7
1940 62.9
1950 68.2
1960 69.7
1970 70.8
1980 73.7
1985 74.7
1990 75.4
1995 75.8
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Chapter 4 68 Glencoe Algebra 1
4 SCORE Standardized Test Practice(Chapters 1–4)
1. If a = 2, b = 6, and c = 4, then (4a - b) 2 −
(b + c) = ? (Lesson 1-2)
A 4 B 0.4 C 40 D 0.04 1. A B C D
2. If 4 + 7 + 6 = 4 + 7 + 6 + n, what is the value of n? (Lesson 1-3)
F 0 G 1 H 4 J 6 2. F G H J
3. Lynn has 4 more books than José. If Lynn gives José 6 of her books, how many more will José have than Lynn? (Lesson 1-2)
A 2 B 4 C 8 D 10 3. A B C D
4. If x = 16 −
24 , which value of x does not form a proportion? (Lesson 2-6)
F 2 −
3 G 3 −
4 H 12 −
18 J 32 −
48 4. F G H J
5. Two-thirds of a number added to itself is 20. What is the number?
(Lesson 2-1)
A 12 B 13 C 30 D 33 5. A B C D
6. 16% of 980 is 9.8% of what number? (Lesson 2-4)
F 1.6 G 16 H 160 J 1600 6. F G H J
7. For what value(s) of r is 3r - 6 = 7 + 3r? (Lesson 2-7)
A all numbers C 0 B all negative integers D no values of r 7. A B C D
8. The range of a relation includes the integers x −
4 , x −
5 , and x −
8 .
What could be a value for x in the domain? (Lesson 1-6)
F 20 G 30 H 32 J 40 8. F G H J
9. A line with a slope of -1 passes through points at (2, 3) and (5, y). Find the value of y. (Lesson 3-3)
A -6 B -3 C 0 D 6 9. A B C D
10. If a line passes through (0, -6) and has a slope of -3, what is an equation for the line? (Lesson 4-2)
F y = -6x - 3 H y = -3x - 6 G x = -6y - 3 J x = -3y - 6 10. F G H J
Part 1: Multiple Choice
Instructions: Fill in the appropriate circle for the best answer.
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Chapter 4 69 Glencoe Algebra 1
4 Standardized Test Practice (continued)
11. If f (x) = 21 - 6x −
5 , find f -1 (x).
A f -1 (x) = 5x - 21 −
6 C f -1 (x) = 21 + 5x −
6
B f -1 (x) = 21 - 5x −
6 D f -1 (x) = 21 - 6x −
5 11. A B C D
12. If x + 2x + 3x −
2 = 6, x = ? (Lesson 2-3)
F 1 −
2 G 1 H 2 J 4 12. F G H J
13. Find the slope of the line that passes through (2, 2) and (7, 7). (Lesson 3-3)
A -1 B 1 C -5 D 5 13. A B C D
14. What is an equation of the line that passes through (1, 2) and (0, –1)? (Lesson 4-2)
F y = x – 3 G y = – x + 3 H y = – 3x + 1 J y = 3x – 1 14. F G H J
15. The formula for the volume of a rectangular solid is V = Bh. A packing crate has a height of 4.5 inches and a base area of 18.2 square inches. What is the volume of the crate in cubic inches? (Lesson 2-8)
16. Find the slope of a line parallel to the
graph of 1 −
2 y = x + 6. (Lesson 4-4)
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
. . . . .
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
. . . . .
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
Part 2: Gridded Response
Instructions: Enter your answers by writing each digit of the answer in a column box
and then shading in the appropriate circle that corresponds to that entry.
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Chapter 4 70 Glencoe Algebra 1
4 Standardized Test Practice (continued)
17. Write 2 � r � r � t � t using exponents. (Lesson 1-1)
18. Evaluate 2xy - y2 if x = 6 and y = 12. (Lesson 1-2)
Simplify each expression. (Lessons 1-2 through 1-5)
19. 12 - 6 × 5 20. 6(2 + 3) - 9
21. (2 � 3)2 - 22 22. 4 � 9 - 2 � 10
23. 4(2y + y) - 6(4y + 3y) 24. 12a - 18b −
-6
For Questions 25–27, solve each equation. (Lessons 2-2 and 2-3)
25. 13 - m = 21
26. 3 −
4 x = 2 −
3
27. 4x + 12 = -16
28. Solve x - 2y = 12 if the domain is {-3, -1, 0, 2, 5}.(Lesson 3-1)
29. Determine whether {(1, 4), (2, 6), (3, 7), (4, 4)} is a function, and explain your reasoning. (Lesson 1-7)
30. Write an equation for the relationship between the variables in the chart. (Lesson 3-6)
x 0 2 4 6
y 2 5 8 11
31. Determine the slope of the line passing through (2, 7) and (-5, 2). (Lesson 4-3)
32. Write an equation in slope-intercept form for the line passing through (2, 6) with a slope of -3. (Lesson 4-1)
33. Write an equation for the line passing through (-6, 5) and (-6, -4). (Lesson 4-2)
34. Lucy owns a bakery. In 2006, she sold pies for $9.50 each. In 2010, she sold pies for $17.50 each. (Lesson 3-3)
a. Find the rate of change for the price of a pie from 2006 to 2010.
b. How much do you think Lucy will sell a pie for in 2014?
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34a.
34b.
Part 3: Short Response
Instructions: Write your answers in the space.
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Chapter 4 A1 Glencoe Algebra 1
Chapter Resources
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
4
Cha
pte
r 4
3 G
lenc
oe A
lgeb
ra 1
Ant
icip
atio
n G
uide
Eq
uati
on
s o
f Lin
ear
Fu
ncti
on
s
B
efor
e yo
u b
egin
Ch
ap
ter
4
•
Rea
d ea
ch s
tate
men
t.
•
Dec
ide
wh
eth
er y
ou A
gree
(A
) or
Dis
agre
e (D
) w
ith
th
e st
atem
ent.
•
Wri
te A
or
D i
n t
he
firs
t co
lum
n O
R i
f yo
u a
re n
ot s
ure
wh
eth
er y
ou a
gree
or
disa
gree
, wri
te N
S (
Not
Su
re).
A
fter
you
com
ple
te C
ha
pte
r 4
•
Rer
ead
each
sta
tem
ent
and
com
plet
e th
e la
st c
olu
mn
by
ente
rin
g an
A o
r a
D.
•
Did
an
y of
you
r op
inio
ns
abou
t th
e st
atem
ents
ch
ange
fro
m t
he
firs
t co
lum
n?
•
For
th
ose
stat
emen
ts t
hat
you
mar
k w
ith
a D
, use
a p
iece
of
pape
r to
wri
te a
n
exam
ple
of w
hy
you
dis
agre
e.
ST
EP
1A
, D, o
r N
SS
tate
men
tS
TE
P 2
A o
r D
1.
Th
e sl
ope
of a
lin
e gi
ven
by
an e
quat
ion
in
th
e fo
rm y
= m
x +
b
can
be
dete
rmin
ed b
y lo
okin
g at
th
e eq
uat
ion
. 2
. T
he
y-in
terc
ept
of y
= 1
2x -
8 i
s 8.
3.
If t
wo
poin
ts o
n a
lin
e ar
e kn
own
, th
en a
n e
quat
ion
can
be
wri
tten
for
th
at l
ine.
4.
An
equ
atio
n i
n t
he
form
y =
mx
+ b
is
in p
oin
t-sl
ope
form
. 5
. If
a p
air
of l
ines
are
par
alle
l, th
en t
hey
hav
e th
e sa
me
slop
e. 6
. L
ines
th
at i
nte
rsec
t at
rig
ht
angl
es a
re c
alle
d pe
rpen
dicu
lar
lin
es.
7.
A s
catt
er p
lot
is s
aid
to h
ave
a n
egat
ive
corr
elat
ion
wh
en t
he
poin
ts a
re r
ando
m a
nd
show
no
rela
tion
ship
bet
wee
n x
an
d y.
8.
Th
e cl
oser
th
e co
rrel
atio
n c
oeff
icie
nt
is t
o ze
ro, t
he
mor
e cl
osel
y a
best
-fit
lin
e m
odel
s a
set
of d
ata.
9.
Th
e eq
uat
ion
s of
a r
egre
ssio
n l
ine
and
a m
edia
n-f
it l
ine
are
very
sim
ilar
.
10.
An
in
vers
e re
lati
on i
s ob
tain
ed b
y ex
chan
gin
g th
e x-
coor
din
ates
w
ith
th
e y-
coor
din
ates
of
each
ord
ered
pai
r of
th
e or
igin
al
rela
tion
.
Step
1
Step
2
A D D AA A D D A A
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M
Answers (Anticipation Guide and Lesson 4-1)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 4-1
4-1
Cha
pte
r 4
5 G
lenc
oe A
lgeb
ra 1
Stud
y G
uide
and
Inte
rven
tion
Gra
ph
ing
Eq
uati
on
s i
n S
lop
e-I
nte
rcep
t Fo
rm
Slo
pe-
Inte
rcep
t Fo
rmS
lop
e-In
terc
ept
Form
y =
mx
+ b
, w
he
re m
is t
he
slo
pe
an
d b
is t
he
y-in
terc
ep
t
W
rite
an
eq
uat
ion
in
slo
pe-
inte
rcep
t fo
rm f
or t
he
lin
e w
ith
a s
lop
e of
-4
and
a y
-in
terc
ept
of 3
.
y =
mx
+ b
S
lope-inte
rcept
form
y =
-4x
+ 3
R
epla
ce m
with -
4 a
nd b
with 3
.
G
rap
h 3
x -
4y
= 8
.
3x -
4y
= 8
O
rigin
al equation
-
4y =
-3x
+ 8
S
ubtr
act
3x
from
each s
ide.
-
4y
−
-4
= -
3x +
8
−
-4
D
ivid
e e
ach s
ide b
y -
4.
y
= 3 −
4 x -
2
Sim
plif
y.
Th
e y-
inte
rcep
t of
y =
3 −
4 x -
2 i
s -
2 an
d th
e sl
ope
is 3 −
4 . S
o gr
aph
th
e po
int
(0, -
2). F
rom
th
is p
oin
t, m
ove
up
3 u
nit
s an
d ri
ght
4 u
nit
s. D
raw
a l
ine
pass
ing
thro
ugh
bot
h p
oin
ts.
Exer
cise
sW
rite
an
eq
uat
ion
of
a li
ne
in s
lop
e-in
terc
ept
form
wit
h t
he
give
n s
lop
e an
d
y-in
terc
ept.
1. s
lope
: 8, y
-in
terc
ept
-3
2. s
lope
: -2,
y-i
nte
rcep
t -
1 3.
slo
pe: -
1, y
-in
terc
ept
-7
y
= 8
x -
3
y =
-2x
- 1
y
= -
x -
7
Wri
te a
n e
qu
atio
n i
n s
lop
e-in
terc
ept
form
for
eac
h g
rap
h s
how
n.
4.
( 0, –
2)
( 1, 0
)x
y
O
5.
( 3, 0
)
( 0, 3
)
x
y
O
6.
( 4, –
2)
( 0, –
5)
xy
O
y
= 2
x -
2
y =
-x +
3
y =
3 −
4 x -
5
Gra
ph
eac
h e
qu
atio
n.
7. y
= 2
x +
1
8. y
= -
3x +
2
9. y
= -
x -
1
x
y
O
x
y
O
x
y
O
( 0, –
2)
( 4, 1
)
x
y
O
3x -
4y
= 8
Exam
ple
1
Exam
ple
2
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-Hill, a d
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PDF Pass
Chapter 4 A2 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
4-1
Cha
pte
r 4
6 G
lenc
oe A
lgeb
ra 1
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nu
ed)
Gra
ph
ing
Eq
uati
on
s i
n S
lop
e-I
nte
rcep
t Fo
rm
Mo
del
ing
Rea
l-W
orl
d D
ata
MED
IA S
ince
199
9, t
he
nu
mb
er o
f m
usi
c ca
sset
tes
sold
has
d
ecre
ased
by
an a
vera
ge r
ate
of 2
7 m
illi
on p
er y
ear.
Th
ere
wer
e 12
4 m
illi
on m
usi
c ca
sset
tes
sold
in
199
9.
a.
Wri
te a
lin
ear
equ
atio
n t
o fi
nd
th
e av
erag
e n
um
ber
of
mu
sic
cass
ette
s so
ld i
n
any
year
aft
er 1
999.
T
he
rate
of
chan
ge i
s -
27 m
illi
on p
er y
ear.
In t
he
firs
t ye
ar, t
he
nu
mbe
r of
mu
sic
cass
ette
s so
ld w
as 1
24 m
illi
on. L
et N
= t
he
nu
mbe
r of
mil
lion
s of
mu
sic
cass
ette
s so
ld.
Let
x =
th
e n
um
ber
of y
ears
sin
ce 1
999.
An
equ
atio
n i
s N
= -
27x
+ 1
24.
b.
Gra
ph
th
e eq
uat
ion
.
Th
e gr
aph
of
N =
-27
x +
124
is
a li
ne
that
pas
ses
thro
ugh
th
e po
int
at (
0, 1
24)
and
has
a s
lope
of
-27
.
c.
Fin
d t
he
app
roxi
mat
e n
um
ber
of
mu
sic
cass
ette
s so
ld i
n 2
003.
N
= -
27x
+ 1
24
Ori
gin
al equation
N
= -
27(4
) +
124
R
epla
ce x
with 4
.
N
= 1
6 S
implif
y.
T
her
e w
ere
abou
t 16
mil
lion
mu
sic
cass
ette
s so
ld i
n 2
003.
Exer
cise
s 1
. MU
SIC
In
200
1, f
ull
-len
gth
cas
sett
es r
epre
sen
ted
3.4%
of
tota
l m
usi
c sa
les.
Bet
wee
n 2
001
and
2006
, th
e pe
rcen
t de
crea
sed
by a
bou
t 0.
5% p
er y
ear.
a. W
rite
an
equ
atio
n t
o fi
nd
the
perc
ent
P o
f re
cord
ed m
usi
c so
ld a
s fu
ll-l
engt
h c
asse
ttes
for
an
y ye
ar x
bet
wee
n
2001
an
d 20
06.
b.
Gra
ph t
he
equ
atio
n o
n t
he
grid
at
the
righ
t.c.
Fin
d th
e pe
rcen
t of
rec
orde
d m
usi
c so
ld
as f
ull
-len
gth
cas
sett
es i
n 2
004.
2. P
OPU
LATI
ON
Th
e po
pula
tion
of
the
Un
ited
Sta
tes
is
proj
ecte
d to
be
300
mil
lion
by
the
year
201
0. B
etw
een
20
10 a
nd
2050
, th
e po
pula
tion
is
expe
cted
to
incr
ease
by
abo
ut
2.5
mil
lion
per
yea
r.a.
Wri
te a
n e
quat
ion
to
fin
d th
e po
pula
tion
P i
n a
ny
year
x
betw
een
201
0 an
d 20
50.
b.
Gra
ph t
he
equ
atio
n o
n t
he
grid
at
the
righ
t.
c. F
ind
the
popu
lati
on i
n 2
050.
ab
ou
t 40
0,0
00,
00
0
Full-
leng
th C
asse
tte
Sale
s
Percent of Total Music Sales
1.5%
2.0%
1.0%
2.5%
3.0%
3.5%
Year
s Si
nce
2001
32
10
54
Proj
ecte
d Un
ited
Stat
es P
opul
atio
n
Year
s Si
nce
2010
Population (millions)
020
40x
P
400
380
360
340
320
300
Mus
ic C
asse
ttes
Sol
d
Cassettes (millions)
5075 25
0
100
125
Year
s Si
nce
1999
32
15
74
6
Exam
ple
P =
-0.
5x +
3.4 1.9%
P =
2,5
00,
00
0x +
30
0,0
00,
00
0
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Lesson X-1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 4-1
4-1
Cha
pte
r 4
7 G
lenc
oe A
lgeb
ra 1
Skill
s Pr
acti
ceG
rap
hin
g E
qu
ati
on
s i
n S
lop
e-I
nte
rcep
t Fo
rmW
rite
an
eq
uat
ion
of
a li
ne
in s
lop
e-in
terc
ept
form
wit
h t
he
give
n s
lop
e an
d y
-in
terc
ept.
1. s
lope
: 5, y
-in
terc
ept:
-3
y =
5x -
3
2. s
lope
: -2,
y-i
nte
rcep
t: 7
y =
-2x
+ 7
3. s
lope
: -6,
y-i
nte
rcep
t: -
2 y =
-6x
- 2
4.
slo
pe: 7
, y-i
nte
rcep
t: 1
y =
7x +
1
5. s
lope
: 3, y
-in
terc
ept:
2 y
= 3
x +
2
6. s
lope
: -4,
y-i
nte
rcep
t: -
9 y =
-4x
- 9
7. s
lope
: 1, y
-in
terc
ept:
-12
y =
x -
12
8. s
lope
: 0, y
-in
terc
ept:
8 y
= 8
Wri
te a
n e
qu
atio
n i
n s
lop
e-in
terc
ept
form
for
eac
h g
rap
h s
how
n.
9.
( 2, 1
)
( 0, –
3)
x
y
O
10
.
( 0, 2
)
( 2, –
4)
x
y
O
11
.
( 0, –
1)( 2
, –3)
x
y O
y
= 2
x -
3
y =
-3x
+ 2
y
= -
x -
1
Gra
ph
eac
h e
qu
atio
n.
12. y
= x
+ 4
13
. y =
-2x
- 1
14
. x +
y =
-3
x
y
O
x
y
O
x
y
O
15. V
IDEO
REN
TALS
A v
ideo
sto
re c
har
ges
$10
for
a re
nta
l ca
rd
plu
s $2
per
ren
tal.
a. W
rite
an
equ
atio
n i
n s
lope
-in
terc
ept
form
for
th
e to
tal
cost
c o
f bu
yin
g a
ren
tal
card
an
d re
nti
ng
m
mov
ies.
b.
Gra
ph t
he
equ
atio
n.
c. F
ind
the
cost
of
buyi
ng
a re
nta
l ca
rd a
nd
ren
tin
g 6
mov
ies.
$2
2
Vide
o St
ore
Rent
al C
osts
Total Cost ($)
10 01214161820c
Mov
ies
Rent
ed1
23
45
m
c =
10
+ 2m
c =
10
+ 2
m
001_
012_
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Answers (Lesson 4-1)
A01-A12_ALG1_A_CRM_C04_AN_660499.indd A2A01-A12_ALG1_A_CRM_C04_AN_660499.indd A2 12/21/10 1:23 AM12/21/10 1:23 AM
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pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 4 A3 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
4-1
Cha
pte
r 4
8 G
lenc
oe A
lgeb
ra 1
Prac
tice
Gra
ph
ing
Eq
uati
on
s i
n S
lop
e-I
nte
rcep
t Fo
rmW
rite
an
eq
uat
ion
of
a li
ne
in s
lop
e-in
terc
ept
form
wit
h t
he
give
n s
lop
e an
d
y-in
terc
ept.
1. s
lope
: 1 −
4 , y-
inte
rcep
t: 3
y =
1 −
4 x +
3
2. s
lope
: 3 −
2 , y-
inte
rcep
t: -
4 y =
3 −
2 x -
4
3. s
lope
: 1.5
, y-i
nte
rcep
t: -
1 4.
slo
pe: -
2.5,
y-i
nte
rcep
t: 3
.5
y
= 1
.5x -
1
y =
-2.
5x +
3.5
Wri
te a
n e
qu
atio
n i
n s
lop
e-in
terc
ept
form
for
eac
h g
rap
h s
how
n.
5.
( –5,
0)
( 0, 2
)
x
y
O
6.
( –2,
0)
( 0, 3
)
x
y O
7.
( –3,
0)
( 0, –
2)
x
y
O
y =
2 −
5 x +
2
y =
3 −
2 x +
3
y =
-
2 −
3 x -
2
Gra
ph
eac
h e
qu
atio
n.
8. y
= -
1 −
2 x +
2
9. 3
y =
2x
- 6
10
. 6x
+ 3
y =
6
x
y
O
x
y
O
x
y
O
11. W
RIT
ING
Car
la h
as a
lrea
dy w
ritt
en 1
0 pa
ges
of a
nov
el.
Sh
e pl
ans
to w
rite
15
addi
tion
al p
ages
per
mon
th u
nti
l sh
e is
fin
ish
ed.
a. W
rite
an
equ
atio
n t
o fi
nd
the
tota
l n
um
ber
of p
ages
P
wri
tten
aft
er a
ny
nu
mbe
r of
mon
ths
m.
P =
10
+ 1
5m
b.
Gra
ph t
he
equ
atio
n o
n t
he
grid
at
the
righ
t.
c. F
ind
the
tota
l n
um
ber
of p
ages
wri
tten
aft
er 5
mon
ths.
85
Carl
a’s
Nov
el
Mon
ths
Pages Written
20
46
13
5m
P
100 80 60 40 20
001_
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 4-1
4-1
Cha
pte
r 4
9 G
lenc
oe A
lgeb
ra 1
Wor
d Pr
oble
m P
ract
ice
Gra
ph
ing
Eq
uati
on
s i
n S
lop
e-I
nte
rcep
t Fo
rm
1.SA
VIN
GS
Wad
e’s
gran
dmot
her
gav
e h
im
$100
for
his
bir
thda
y. W
ade
wan
ts t
o sa
ve h
is m
oney
to
buy
a n
ew M
P3
play
er
that
cos
ts $
275.
Eac
h m
onth
, he
adds
$2
5 to
his
MP
3 sa
vin
gs. W
rite
an
eq
uat
ion
in
slo
pe-i
nte
rcep
t fo
rm f
or x
, th
e n
um
ber
of m
onth
s th
at i
t w
ill
take
Wad
e to
sav
e $2
75.
2
75 =
25x
+ 1
00
2. C
AR
CA
RE
Su
ppos
e re
gula
r ga
soli
ne
cost
s $2
.76
per
gall
on. Y
ou c
an p
urc
has
e a
car
was
h a
t th
e ga
s st
atio
n f
or $
3. T
he
grap
h o
f th
e eq
uat
ion
for
th
e co
st o
f x
gall
ons
of g
asol
ine
and
a ca
r w
ash
is
show
n b
elow
. Wri
te t
he
equ
atio
n i
n s
lope
-in
terc
ept
form
for
th
e li
ne.
Gas
olin
e (g
al)
32
10
54
98
710
y
x6
Cost of gas and car wash ($)
68 4 21016 14 121824 22 20
( 4, 1
4.04
)
( 2, 8
.52)
( 0, 3
)
y=
2.7
6x+
3
3. A
DU
LT E
DU
CA
TIO
N A
ngi
e’s
mot
her
w
ants
to
take
som
e ad
ult
edu
cati
on
clas
ses
at t
he
loca
l h
igh
sch
ool.
Sh
e h
as
to p
ay a
on
e-ti
me
enro
llm
ent
fee
of $
25
to jo
in t
he
adu
lt e
duca
tion
com
mu
nit
y,
and
then
$45
for
eac
h c
lass
sh
e w
ants
to
take
. Th
e eq
uat
ion
y =
45x
+ 2
5 ex
pres
ses
the
cost
of
taki
ng
x cl
asse
s.
Wh
at a
re t
he
slop
e an
d y-
inte
rcep
t of
th
e eq
uat
ion
?
m
= 4
5; y
-in
terc
ept
= 2
5
4.B
USI
NES
S A
con
stru
ctio
n c
rew
nee
ds t
o re
nt
a tr
ench
dig
ger
for
up
to a
wee
k. A
n
equ
ipm
ent
ren
tal
com
pan
y ch
arge
s $4
0 pe
r da
y pl
us
a $2
0 n
on-r
efu
nda
ble
insu
ran
ce c
ost
to r
ent
a tr
ench
dig
ger.
Wri
te a
nd
grap
h a
n e
quat
ion
to
fin
d th
e to
tal
cost
to
ren
t th
e tr
ench
dig
ger
for
d d
ays.
Day
s3
21
05
49
87
6
Price ($)
100
140 60 20180
300
340
260
220
5. E
NER
GY
Fro
m 2
002
to 2
005,
U.S
. co
nsu
mpt
ion
of
ren
ewab
le e
ner
gy
incr
ease
d an
ave
rage
of
0.17
qu
adri
llio
n
BT
Us
per
year
. Abo
ut
6.07
qu
adri
llio
n
BT
Us
of r
enew
able
pow
er w
ere
prod
uce
d in
th
e ye
ar 2
002.
a. W
rite
an
equ
atio
n i
n s
lope
-in
terc
ept
form
to
fin
d th
e am
oun
t of
ren
ewab
le
pow
er P
(qu
adri
llio
n B
TU
s) p
rodu
ced
in y
ear
y be
twee
n 2
002
and
2005
. P
= 0
.17y
+ 6
.07
b.
App
roxi
mat
ely
how
mu
ch r
enew
able
po
wer
was
pro
duce
d in
200
5?6.
58 q
uad
rilli
on
BT
Us
c. I
f th
e sa
me
tren
d co
nti
nu
es f
rom
200
6 to
201
0, h
ow m
uch
ren
ewab
le p
ower
w
ill
be p
rodu
ced
in t
he
year
201
0?
7.43
qu
adri
llio
n B
TU
s
y =
40d
+ 2
0
001_
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M
Answers (Lesson 4-1)
A01-A12_ALG1_A_CRM_C04_AN_660499.indd A3A01-A12_ALG1_A_CRM_C04_AN_660499.indd A3 12/21/10 1:24 AM12/21/10 1:24 AM
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pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 4 A4 Glencoe Algebra 1
Lesson X-2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 4-2
4-2
Cha
pte
r 4
11
Gle
ncoe
Alg
ebra
1
Exer
cise
sW
rite
an
eq
uat
ion
of
the
lin
e th
at p
asse
s th
rou
gh t
he
give
n p
oin
t an
d h
as t
he
give
n s
lop
e.
1.
( 3, 5
)
x
y
O
m =
2
2.
( 0, 0
)x
y
O
m =
–2
3.
( 2, 4
)
x
y
O
m =
1 2
y
= 2
x -
1
y =
-2x
y
= 1 −
2 x +
3
4. (
8, 2
); sl
ope
-
3 −
4 5.
(-
1, -
3); s
lope
5
6. (
4, -
5); s
lope
-
1 −
2
y
= -
3 −
4 x +
8
y =
5x +
2
y =
-
1 −
2 x -
3
7. (
-5,
4);
slop
e 0
8. (
2, 2
); sl
ope
1 −
2 9.
(1,
-4)
; slo
pe -
6
y
= 4
y
= 1 −
2 x +
1
y =
-6x
+ 2
10. (
-3,
0),
m =
2
11. (
0, 4
), m
= -
3 12
. (0,
350
), m
= 1
−
5
y
= 2
x +
6
y =
-3x
+ 4
y
= 1 −
5 x +
350
Stud
y G
uide
and
Inte
rven
tion
Wri
tin
g E
qu
ati
on
s i
n S
lop
e-I
nte
rcep
t Fo
rm
Wri
te a
n E
qu
atio
n G
iven
th
e Sl
op
e an
d a
Po
int
W
rite
an
eq
uat
ion
of
the
lin
e th
at p
asse
s th
rou
gh (
-4,
2)
wit
h a
slo
pe
of 3
.T
he
lin
e h
as s
lope
3. T
o fi
nd
the
y-in
terc
ept,
rep
lace
m w
ith
3 a
nd
(x, y
) w
ith
(-
4, 2
) in
th
e sl
ope-
inte
rcep
t fo
rm.
Th
en s
olve
for
b.
y =
mx
+ b
S
lope-inte
rcept
form
2 =
3(-
4) +
b
m =
3,
y =
2,
and x
= -
4
2 =
-12
+ b
M
ultip
ly.
14 =
b
Add 1
2 t
o e
ach s
ide.
Th
eref
ore,
th
e eq
uat
ion
is
y =
3x
+ 1
4.
W
rite
an
eq
uat
ion
of
the
lin
eth
at p
asse
s th
rou
gh (
-2,
-1)
wit
h a
sl
ope
of 1 −
4 .T
he
lin
e h
as s
lope
1 −
4 . R
epla
ce m
wit
h 1 −
4 an
d (x
, y)
wit
h (
-2,
-1)
in
th
e sl
ope-
inte
rcep
t fo
rm.
y
= m
x +
b
Slo
pe-inte
rcept
form
-1
= 1 −
4 (-
2) +
b
m =
1 −
4 , y =
-1,
and x
= -
2
-1
= -
1 −
2 + b
M
ultip
ly.
- 1 −
2 = b
A
dd 1
−
2 to
each s
ide.
Th
eref
ore,
th
e eq
uat
ion
is
y =
1 −
4 x -
1 −
2 .
Exam
ple
1Ex
amp
le 2
001_
012_
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M
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
4-1
Cha
pte
r 4
10
Gle
ncoe
Alg
ebra
1
Enri
chm
ent
Usin
g E
qu
ati
on
s: Id
eal W
eig
ht
You
can
fin
d yo
ur
idea
l w
eigh
t as
fol
low
s.A
wom
an s
hou
ld w
eigh
100
pou
nds
for
th
e fi
rst
5 fe
et o
f h
eigh
t an
d 5
addi
tion
al p
oun
ds f
or e
ach
in
ch o
ver
5 fe
et (
5 fe
et =
60
inch
es).
A m
an s
hou
ld w
eigh
106
pou
nds
for
th
e fi
rst
5 fe
et o
f h
eigh
t an
d 6
addi
tion
al p
oun
ds f
or e
ach
in
ch o
ver
5 fe
et. T
hes
e fo
rmu
las
appl
y to
pe
ople
wit
h n
orm
al b
one
stru
ctu
res.
To
dete
rmin
e yo
ur
bon
e st
ruct
ure
, wra
p yo
ur
thu
mb
and
inde
x fi
nge
r ar
oun
d th
e w
rist
of
you
r ot
her
han
d. I
f th
e th
um
b an
d fi
nge
r ju
st t
ouch
, yo
u h
ave
nor
mal
bon
e st
ruct
ure
. If
they
ove
rlap
, you
are
sm
all-
bon
ed.
If t
hey
don
’t ov
erla
p, y
ou a
re l
arge
-bon
ed. S
mal
l-bo
ned
peo
ple
shou
ld d
ecre
ase
thei
r ca
lcu
late
d id
eal
wei
ght
by 1
0%. L
arge
-bon
ed p
eopl
e sh
ould
in
crea
se t
he
valu
e by
10%
.
Cal
cula
te t
he
idea
l w
eigh
ts o
f th
ese
peo
ple
.1.
wom
an, 5
ft
4 in
., n
orm
al-b
oned
2.
man
, 5 f
t 11
in
., la
rge-
bon
ed
120
lb
189
.2 lb
3. m
an, 6
ft
5 in
., sm
all-
bon
ed
4. y
ou, i
f yo
u a
re a
t le
ast
5 ft
tal
l
187
.2 lb
A
nsw
ers
will
var
y.
For
Exe
rcis
es 5
–9, u
se t
he
foll
owin
g in
form
atio
n.
Su
ppos
e a
nor
mal
-bon
ed m
an i
s x
inch
es t
all.
If h
e is
at
leas
t 5
feet
ta
ll, t
hen
x -
60
repr
esen
ts t
he
nu
mbe
r of
in
ches
th
is m
an i
s ov
er
5 fe
et t
all.
For
eac
h o
f th
ese
inch
es, h
is i
deal
wei
ght
is i
ncr
ease
d by
6
pou
nds
. Th
us,
his
pro
per
wei
ght
y is
giv
en b
y th
e fo
rmu
la
y =
6(x
- 6
0) +
106
or
y =
6x
- 2
54. I
f th
e m
an i
s la
rge-
bon
ed, t
he
form
ula
bec
omes
y =
6x
- 2
54 +
0.1
0(6x
- 2
54).
5. W
rite
th
e fo
rmu
la f
or t
he
wei
ght
of a
lar
ge-b
oned
man
in
slo
pe-i
nte
rcep
t fo
rm.
6. D
eriv
e th
e fo
rmu
la f
or t
he
idea
l w
eigh
t y
of a
nor
mal
-bon
ed
fem
ale
wit
h h
eigh
t x
inch
es. W
rite
th
e fo
rmu
la i
n
slop
e-in
terc
ept
form
.
7. D
eriv
e th
e fo
rmu
la i
n s
lope
-in
terc
ept
form
for
th
e id
eal
wei
ght
y of
a l
arge
-bon
ed f
emal
e w
ith
hei
ght
x in
ches
.
8. D
eriv
e th
e fo
rmu
la i
n s
lope
-in
terc
ept
form
for
th
e id
eal
wei
ght
y of
a s
mal
l-bo
ned
mal
e w
ith
hei
ght
x in
ches
.
9. F
ind
the
hei
ghts
at
wh
ich
th
e id
eal
wei
ghts
of
nor
mal
-bon
ed m
ales
and
larg
e-bo
ned
fem
ales
wou
ld b
e th
e sa
me.
y =
6.6
x -
279
.4
y =
5x -
20
0
y =
5.5
x -
220
y =
5.4
x -
228
.6
68 in
., o
r 5
ft 8
in.
001_
012_
ALG
1_A
_CR
M_C
04_C
R_6
6049
9.in
dd
1012
/21/
10
12:4
5 A
M
Answers (Lesson 4-1 and Lesson 4-2)
A01-A12_ALG1_A_CRM_C04_AN_660499.indd A4A01-A12_ALG1_A_CRM_C04_AN_660499.indd A4 12/21/10 1:24 AM12/21/10 1:24 AM
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pyr
ight
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lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 4 A5 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
4-2
Cha
pte
r 4
12
Gle
ncoe
Alg
ebra
1
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nu
ed)
Wri
tin
g E
qu
ati
on
s i
n S
lop
e-I
nte
rcep
t Fo
rm
Wri
te a
n E
qu
atio
n G
iven
Tw
o P
oin
ts
W
rite
an
eq
uat
ion
of
the
lin
e th
at p
asse
s th
rou
gh (
1, 2
) an
d (
3, -
2).
Fin
d th
e sl
ope
m. T
o fi
nd
the
y-in
terc
ept,
rep
lace
m w
ith
its
com
pute
d va
lue
and
(x, y
) w
ith
(1
, 2)
in t
he
slop
e-in
terc
ept
form
. Th
en s
olve
for
b.
m =
y 2 -
y 1
−
x 2 -
x 1
Slo
pe form
ula
m =
-2
- 2
−
3 -
1
y 2 =
-2,
y 1 =
2,
x 2 =
3,
x 1 =
1
m =
-2
Sim
plif
y.
y =
mx
+ b
S
lope-inte
rcept
form
2 =
-2(
1) +
b
Repla
ce m
with -
2,
y w
ith 2
, and x
with 1
.
2 =
-2
+ b
M
ultip
ly.
4 =
b
Add 2
to e
ach s
ide.
Th
eref
ore,
th
e eq
uat
ion
is
y =
-2x
+ 4
.
Exer
cise
sW
rite
an
eq
uat
ion
of
the
lin
e th
at p
asse
s th
rou
gh e
ach
pai
r of
poi
nts
.
1.
( 1, 1
)
( 0, –
3)
x
y
O
2.
( 0
, 4) ( 4
, 0)
x
y
O
3.
( 0, 1
)
( –3,
0)
x
y
O
y
= 4
x -
3
y =
-x +
4
y =
1 −
3 x +
1
4. (
-1,
6),
(7, -
10)
5. (
0, 2
), (1
, 7)
6. (
6, -
25),
(-1,
3)
y
= -
2x +
4
y =
5x +
2
y =
-4x
- 1
7. (
-2,
-1)
, (2,
11)
8.
(10
, -1)
, (4,
2)
9. (
-14
, -2)
, (7,
7)
y
= 3
x +
5
y =
-
1 −
2 x +
4
y =
3 −
7 x +
4
10. (
4, 0
), (0
, 2)
11. (
-3,
0),
(0, 5
) 12
. (0,
16)
, (-
10, 0
)
y
= -
1 −
2 x +
2
y =
5 −
3 x +
5
y =
8 −
5 x +
16
Exam
ple
001_
012_
ALG
1_A
_CR
M_C
04_C
R_6
6049
9.in
dd
1212
/21/
10
12:4
5 A
M
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 4-2
Cha
pte
r 4
13
Gle
ncoe
Alg
ebra
1
Wri
te a
n e
qu
atio
n o
f th
e li
ne
that
pas
ses
thro
ugh
th
e gi
ven
poi
nt
wit
h t
he
give
n s
lop
e.
1.
( –1,
4)
x
y
O
m =
–3
2.
( 4
, 1)
x
y
O
m =
1
3.
( -1,
2)
x
y O
m =
2
y
= -
3x +
1
y =
x -
3
y =
2x +
4
4. (
1, 9
); sl
ope
4 5.
(4,
2);
slop
e -
2 6.
(2,
-2)
; slo
pe 3
y
= 4
x +
5
y =
-2x
+ 1
0 y
= 3
x -
8
7. (
3, 0
); sl
ope
5 8.
(-
3, -
2); s
lope
2
9. (
-5,
4);
slop
e -
4
y =
5x -
15
y =
2x +
4
y =
-4x
- 1
6
Wri
te a
n e
qu
atio
n o
f th
e li
ne
that
pas
ses
thro
ugh
eac
h p
air
of p
oin
ts.
10.
( –2,
3)
( 3, –
2)
x
y
O
11
.
( –1,
–3)
( 1, 1
)x
y
O
12
.
( 2, –
1)
( 0, 3
)
x
y
O
y
= -
x +
1
y =
2x -
1
y =
-2x
+ 3
13. (
1, 3
), (-
3, -
5)
14. (
1, 4
), (6
, -1)
15
. (1,
-1)
, (3,
5)
y
= 2
x +
1
y =
-x +
5
y =
3x -
4
16. (
-2,
4),
(0, 6
) 17
. (3,
3),
(1, -
3)
18. (
-1,
6),
(3, -
2)
y =
x +
6
y =
3x -
6
y =
-2x
+ 4
19. I
NV
ESTI
NG
Th
e pr
ice
of a
sh
are
of s
tock
in
XY
Z C
orpo
rati
on w
as $
74 t
wo
wee
ks a
go.
Sev
en w
eeks
ago
, th
e pr
ice
was
$59
a s
har
e.
a. W
rite
a l
inea
r eq
uat
ion
to
fin
d th
e pr
ice
p of
a s
har
e of
XY
Z C
orpo
rati
on s
tock
w w
eeks
fro
m n
ow.
p =
3w
+ 8
0
b.
Est
imat
e th
e pr
ice
of a
sh
are
of s
tock
fiv
e w
eeks
ago
.$ 6
5
Skill
s Pr
acti
ceW
riti
ng
Eq
uati
on
s i
n S
lop
e-I
nte
rcep
t Fo
rm
4-2
013_
023_
ALG
1_A
_CR
M_C
04_C
R_6
6049
9.in
dd
1312
/21/
10
12:4
6 A
M
Answers (Lesson 4-2)
A01-A12_ALG1_A_CRM_C04_AN_660499.indd A5A01-A12_ALG1_A_CRM_C04_AN_660499.indd A5 12/21/10 1:24 AM12/21/10 1:24 AM
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 4 A6 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 4
14
Gle
ncoe
Alg
ebra
1
Prac
tice
Wri
tin
g E
qu
ati
on
s i
n S
lop
e-I
nte
rcep
t Fo
rm
Wri
te a
n e
qu
atio
n o
f th
e li
ne
that
pas
ses
thro
ugh
th
e gi
ven
poi
nt
and
has
th
e gi
ven
slo
pe.
1.
( 1, 2
)
x
y
O
m =
3
2.
( –2,
2)
x
y O
m =
–2
3.
( –1,
–3)
x
y
O
m =
–1
y
= 3
x -
1
y =
-2x
- 2
y
= -
x -
4
4. (
-5,
4);
slop
e -
3 5.
(4,
3);
slop
e 1 −
2 6.
(1,
-5)
; slo
pe -
3 −
2
y
= -
3x -
11
y =
1 −
2 x +
1
y =
-
3 −
2 x -
7 −
2
7. (
3, 7
); sl
ope
2 −
7 8.
(-
2, 5 −
2 ) ; s
lope
-
1 −
2 9.
(5, 0
); sl
ope
0
y
= 2 −
7 x +
6 1 −
7 y
= -
1 −
2 x +
3 −
2 y
= 0
Wri
te a
n e
qu
atio
n o
f th
e li
ne
that
pas
ses
thro
ugh
eac
h p
air
of p
oin
ts.
10.
( 4, –
2)
( 2, –
4)
x
y
O
11
. ( 0
, 5)
( 4, 1
) x
y
O
12
. ( –
3, 1
)
( –1,
–3)
x
y
O
y
= x
- 6
y
= -
x +
5
y =
-2x
- 5
13. (
0, -
4), (
5, -
4)
14. (
-4,
-2)
, (4,
0)
15. (
-2,
-3)
, (4,
5)
y
= -
4 y
= 1 −
4 x -
1
y =
4 −
3 x -
1 −
3
16. (
0, 1
), (5
, 3)
17. (
-3,
0),
(1, -
6)
18. (
1, 0
), (5
, -1)
y
= 2 −
5 x +
1
y =
-
3 −
2 x -
9 −
2
y =
-
1 −
4 x +
1 −
4
19. D
AN
CE
LESS
ON
S T
he
cost
for
7 d
ance
les
son
s is
$82
. Th
e co
st f
or 1
1 le
sson
s is
$12
2.
Wri
te a
lin
ear
equ
atio
n t
o fi
nd
the
tota
l co
st C
for
ℓ l
esso
ns.
Th
en u
se t
he
equ
atio
n t
o fi
nd
the
cost
of
4 le
sson
s.
20. W
EATH
ER I
t is
76°
F a
t th
e 60
00-f
oot
leve
l of
a m
oun
tain
, an
d 49
°F a
t th
e 12
,000
-foo
t le
vel
of t
he
mou
nta
in. W
rite
a l
inea
r eq
uat
ion
to
fin
d th
e te
mpe
ratu
re T
at
an e
leva
tion
x
on t
he
mou
nta
in, w
her
e x
is i
n t
hou
san
ds o
f fe
et.
C =
10ℓ
+ 1
2; $
52
T =
-4.
5x +
103
4-2
013_
023_
ALG
1_A
_CR
M_C
04_C
R_6
6049
9.in
dd
1412
/21/
10
12:4
6 A
M
Lesson X-2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 4-2
Cha
pte
r 4
15
Gle
ncoe
Alg
ebra
1
Wor
d Pr
oble
m P
ract
ice
Wri
tin
g E
qu
ati
on
s i
n S
lop
e-I
nte
rcep
t Fo
rm
1.FU
ND
RA
ISIN
G Y
von
ne
and
her
fri
ends
h
eld
a ba
ke s
ale
to b
enef
it a
sh
elte
r fo
r h
omel
ess
peop
le. T
he
frie
nds
sol
d 22
cak
es o
n t
he
firs
t da
y an
d 15
cak
es o
n
the
seco
nd
day
of t
he
bake
sal
e. T
hey
co
llec
ted
$88
on t
he
firs
t da
y an
d $6
0 on
th
e se
con
d da
y. L
et x
rep
rese
nt
the
nu
mbe
r of
cak
es s
old
and
y re
pres
ent
the
amou
nt
of m
oney
mad
e. F
ind
the
slop
e of
th
e li
ne
that
wou
ld p
ass
thro
ugh
th
e po
ints
giv
en.
4
2. J
OB
S M
r. K
imba
ll r
ecei
ves
a $3
000
ann
ual
sal
ary
incr
ease
on
th
e an
niv
ersa
ry o
f h
is h
irin
g if
he
rece
ives
a
sati
sfac
tory
per
form
ance
rev
iew
. H
is s
tart
ing
sala
ry w
as $
41,2
50. W
rite
an
equ
atio
n t
o sh
ow k
, Mr.
Kim
ball
’s
sala
ry a
fter
t y
ears
at
this
com
pan
y if
his
per
form
ance
rev
iew
s ar
e al
way
s sa
tisf
acto
ry.
k
= 3
00
0t +
41,
250
3.C
ENSU
S T
he
popu
lati
on o
f L
ared
o,
Tex
as, w
as a
bou
t 21
5,50
0 in
200
7. I
t w
as
abou
t 12
3,00
0 in
199
0. I
f w
e as
sum
e th
at t
he
popu
lati
on g
row
th i
s co
nst
ant
and
t re
pres
ents
th
e n
um
ber
of y
ears
af
ter
1990
, wri
te a
lin
ear
equ
atio
n t
o fi
nd
p, L
ared
o’s
popu
lati
on f
or a
ny
year
af
ter
1990
.
p =
544
1t +
123
,00
0
4.W
ATE
R M
r. W
illi
ams
pays
$40
a m
onth
fo
r ci
ty w
ater
, no
mat
ter
how
man
y ga
llon
s of
wat
er h
e u
ses
in a
giv
en
mon
th. L
et x
rep
rese
nt
the
nu
mbe
r of
ga
llon
s of
wat
er u
sed
per
mon
th. L
et y
repr
esen
t th
e m
onth
ly c
ost
of t
he
city
w
ater
in
dol
lars
. Wh
at i
s th
e eq
uat
ion
of
the
lin
e th
at r
epre
sen
ts t
his
in
form
atio
n?
Wh
at i
s th
e sl
ope
of t
he
lin
e?
y
= 4
0; s
lop
e is
0. T
he
line
is
ho
rizo
nta
l.
5. S
HO
E SI
ZES
Th
e ta
ble
show
s h
ow
wom
en’s
sh
oe s
izes
in
th
e U
nit
ed
Kin
gdom
com
pare
to
wom
en’s
sh
oe s
izes
in
th
e U
nit
ed S
tate
s.
Wo
men
’s S
ho
e S
izes
U.K
.3
3.5
44
.55
5.5
6
U.S
.5
.56
6.5
77.
58
8.5
Sour
ce: D
ance
Spor
t U
K
a. W
rite
a l
inea
r eq
uat
ion
to
dete
rmin
e an
y U
.S. s
ize
y if
you
are
giv
en t
he
U.K
. siz
e x.
y =
x +
2.5
b.
Wh
at a
re t
he
slop
e an
d y-
inte
rcep
t of
th
e li
ne?
slo
pe
= 1
; y
-inte
rcep
t =
2.5
c. I
s th
e y-
inte
rcep
t a
vali
d da
ta p
oin
t fo
r th
e gi
ven
in
form
atio
n?
No
. It
is n
ot
likel
y a
valid
dat
a p
oin
t b
ecau
se t
he
U.K
. siz
ing
p
rob
ably
do
es n
ot
incl
ud
e ze
ro. H
ow
ever
, th
e p
oin
t is
th
e y-i
nte
rcep
t o
f th
e lin
e re
pre
sen
ted
by
the
dat
a if
th
e d
ata
wer
e to
co
nti
nu
e in
defi
nit
ely
in b
oth
dir
ecti
on
s.
4-2
013_
023_
ALG
1_A
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M_C
04_C
R_6
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6 A
M
Answers (Lesson 4-2)
A01-A12_ALG1_A_CRM_C04_AN_660499.indd A6A01-A12_ALG1_A_CRM_C04_AN_660499.indd A6 12/21/10 1:24 AM12/21/10 1:24 AM
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pyr
ight
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oe/
McG
raw
-Hill
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ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 4 A7 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 4
16
Gle
ncoe
Alg
ebra
1
Tan
gen
t to
a C
urv
eA
tan
gen
t li
ne
is a
lin
e th
at i
nte
rsec
ts a
cu
rve
at a
poi
nt
wit
h t
he
sam
e ra
te o
f ch
ange
, or
slop
e, a
s th
e ra
te o
f ch
ange
of
the
curv
e at
th
at p
oin
t.
For
qu
adra
tic
fun
ctio
ns,
fu
nct
ion
s of
th
e fo
rm y
= a
x2 +
bx
+
c,
equ
atio
ns
of t
he
tan
gen
t li
nes
ca
n b
e fo
un
d. T
his
is
base
d on
th
e fa
ct t
hat
th
e sl
ope
thro
ugh
an
y tw
o po
ints
on
th
e cu
rve
is e
qual
to
the
slop
e of
th
e li
ne
tan
gen
t to
th
e cu
rve
at t
he
poin
t w
hos
e x-
valu
e is
hal
fway
be
twee
n t
he
x-va
lues
of
the
oth
er t
wo
poin
ts.
F
ind
an
eq
uat
ion
of
the
lin
e ta
nge
nt
to t
he
curv
e y
= x
2 +
3x
+ 2
th
rou
gh t
he
poi
nt
(2, 1
2).
Fir
st f
ind
two
poin
ts o
n t
he
curv
e w
hos
e x-
valu
es a
re
equ
idis
tan
t fr
om t
he
x-va
lue
of (
2, 1
2).
Ste
p 1
: F
ind
two
poin
ts o
n t
he
curv
e. U
se x
= 1
an
d x
= 3
.
Wh
en x
=
1, y
=
12
+ 3(
1) +
2 o
r 6.
W
hen
x =
3, y
=
32
+ 3
(3)
+ 2
or
20.
S
o, t
he
two
orde
red
pair
s ar
e (1
, 6)
and
(3, 2
0).
Ste
p 2
: F
ind
the
slop
e of
th
e li
ne
that
pas
ses
thro
ugh
th
ese
two
poin
ts.
m
= 20
- 6
−
3 -
1
or 7
Ste
p 3
: N
ow u
se t
his
slo
pe a
nd
the
poin
t (2
, 12)
to
fin
d an
equ
atio
n o
f th
e ta
nge
nt
lin
e.
y =
mx
+ b
S
lope-inte
rcept
form
12
= 7
(2)
+ b
R
epla
ce x
with 2
, y
with 1
2,
and m
with 7
.
-
2 =
b
S
olv
e for
b.
So,
an
equ
atio
n o
f th
e ta
nge
nt
lin
e to
y =
x2
+ 3x
+
2
thro
ugh
th
e po
int
(2, 1
2) i
s y
= 7x
– 2
.
Exer
cise
sF
ind
an
eq
uat
ion
of
the
lin
e ta
nge
nt
to e
ach
cu
rve
thro
ugh
th
e gi
ven
poi
nt.
1. y
= x
2 - 3
x +
7,
(2,
5)
2. y
= 3
x2 + 4
x -
5, (
-4,
27)
3.
y =
5 -
x2 ,
(1, 4
)
y =
x +
3
y =
-20
x -
53
y =
-2x
+ 6
4. F
ind
the
slop
e of
th
e li
ne
tan
gen
t to
th
e cu
rve
at x
= 0
for
th
e ge
ner
al e
quat
ion
y
= a
x2 + b
x +
c.
m
= b
5. F
ind
the
slop
e of
th
e li
ne
tan
gen
t to
th
e cu
rve
y =
ax2 +
bx
+ c
at
x by
fin
din
g th
e sl
ope
of t
he
lin
e th
rou
gh t
he
poin
ts (
0, c
) an
d (2
x, 4
ax2 +
2bx
+ c
). D
oes
this
equ
atio
n f
ind
the
sam
e sl
ope
for
x =
0 a
s yo
u f
oun
d in
Exe
rcis
e 4?
m
= 2
ax +
b, y
es
Enri
chm
ent
y
xO
Exam
ple
4-2
013_
023_
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6 A
M
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 4-3
Cha
pte
r 4
17
Gle
ncoe
Alg
ebra
1
Stud
y G
uide
and
Inte
rven
tion
Wri
tin
g E
qu
ati
on
s i
n P
oin
t-S
lop
e F
orm
Poin
t-Sl
op
e Fo
rm
Po
int-
Slo
pe
Form
y -
y1 =
m(x
- x
1),
wh
ere
(x 1
, y 1
) is
a g
ive
n p
oin
t o
n a
no
nve
rtic
al lin
e
an
d m
is t
he
slo
pe
of
the
lin
e
W
rite
an
eq
uat
ion
in
p
oin
t-sl
ope
form
for
th
e li
ne
that
pas
ses
thro
ugh
(6,
1)
wit
h a
slo
pe
of -
5 −
2 .
y -
y1
= m
(x -
x1)
P
oin
t-slo
pe form
y -
1 =
-
5 −
2 (x -
6)
m =
- 5
−
2 ;
(x1,
y 1)
= (
6,
1)
Th
eref
ore,
th
e eq
uat
ion
is
y -
1 =
-
5 −
2 (x -
6).
W
rite
an
eq
uat
ion
in
p
oin
t-sl
ope
form
for
a h
oriz
onta
l li
ne
that
pas
ses
thro
ugh
(4,
-1)
.
y
- y
1 =
m(x
- x
1)
Poin
t-slo
pe form
y -
(-
1) =
0(x
- 4
) m
= 0
; (x
1,
y 1)
= (
4,
-1)
y
+ 1
= 0
S
implif
y.
Th
eref
ore,
th
e eq
uat
ion
is
y +
1 =
0.
Exer
cise
sW
rite
an
eq
uat
ion
in
poi
nt-
slop
e fo
rm f
or t
he
lin
e th
at p
asse
s th
rou
gh e
ach
poi
nt
wit
h t
he
give
n s
lop
e.
1.
( 4, 1
)
x
y
O
m =
1
2.
( –3,
2)
x
y
O
m =
0
3.
( 2, –
3)
x
y
O
m =
–2
y
- 1
= x
- 4
y
- 2
= 0
y
+ 3
= -
2(x -
2)
4. (
2, 1
), m
= 4
5.
(-7,
2),
m =
6
6. (8
, 3),
m =
1
y -
1 =
4(x
- 2
) y
- 2
= 6
(x +
7)
y -
3 =
x -
8
7. (
-6,
7),
m =
0
8. (4
, 9),
m =
3 −
4 9.
(-4,
-5)
, m =
-
1 −
2
y
- 7
= 0
y
- 9
= 3 −
4 (x -
4)
y +
5 =
-
1 −
2 (x +
4)
10. W
rite
an
equ
atio
n i
n p
oin
t-sl
ope
form
for
a h
oriz
onta
l li
ne
that
pas
ses
thro
ugh
(4
, -2)
.
11. W
rite
an
equ
atio
n i
n p
oin
t-sl
ope
form
for
a h
oriz
onta
l li
ne
that
pas
ses
thro
ugh
(-
5, 6
).
12. W
rite
an
equ
atio
n i
n p
oin
t-sl
ope
form
for
a h
oriz
onta
l li
ne
that
pas
ses
thro
ugh
(5,
0).
y
= 0
Exam
ple
1Ex
amp
le 2
y +
2 =
0
y -
6 =
0
4-3
013_
023_
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M_C
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R_6
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9.in
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6 A
M
Answers (Lesson 4-2 and Lesson 4-3)
A01-A12_ALG1_A_CRM_C04_AN_660499.indd A7A01-A12_ALG1_A_CRM_C04_AN_660499.indd A7 12/21/10 1:24 AM12/21/10 1:24 AM
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 4 A8 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 4
18
Gle
ncoe
Alg
ebra
1
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nu
ed)
Wri
tin
g E
qu
ati
on
s i
n P
oin
t-S
lop
e F
orm
Form
s o
f Li
nea
r Eq
uat
ion
sS
lop
e-In
terc
ept
Form
y =
mx
+ b
m =
slo
pe
; b
= y
-in
terc
ep
t
Po
int-
Slo
pe
Form
y -
y1 =
m(x
- x
1)
m =
slo
pe
; (x
1,
y 1)
is a
giv
en
po
int
Sta
nd
ard
Form
Ax
+ B
y =
CA
an
d B
are
no
t b
oth
ze
ro. U
su
ally
A is n
on
ne
ga
tive
an
d A
, B
, a
nd
C a
re in
teg
ers
wh
ose
gre
ate
st
co
mm
on
fa
cto
r is
1.
W
rite
y +
5 =
2 −
3 (x -
6)
in
stan
dar
d f
orm
.
y
+ 5
= 2 −
3 (x -
6)
Ori
gin
al equation
3(
y +
5)
= 3
( 2 −
3 ) (x
- 6
) M
ultip
ly e
ach s
ide b
y 3
.
3y
+ 1
5 =
2(x
- 6
) D
istr
ibutive
Pro
pert
y
3y
+ 1
5 =
2x
- 1
2 D
istr
ibutive
Pro
pert
y
3y
= 2
x -
27
Subtr
act
15 f
rom
each s
ide.
-2x
+ 3
y =
-27
A
dd -
2x
to e
ach s
ide.
2x
- 3
y =
27
Multip
ly e
ach s
ide b
y -
1.
Th
eref
ore,
th
e st
anda
rd f
orm
of
the
equ
atio
n
is 2
x -
3y
= 2
7.
W
rite
y -
2 =
- 1 −
4 (x -
8)
in
slop
e-in
terc
ept
form
.
y -
2 =
-
1 −
4 (x -
8)
Ori
gin
al equation
y -
2 =
-
1 −
4 x +
2
Dis
trib
utive
Pro
pert
y
y
= -
1 −
4 x +
4
Add 2
to e
ach s
ide.
Th
eref
ore,
th
e sl
ope-
inte
rcep
t fo
rm o
f th
e eq
uat
ion
is
y =
-
1 −
4 x +
4.
Exer
cise
sW
rite
eac
h e
qu
atio
n i
n s
tan
dar
d f
orm
.
1. y
+ 2
= -
3(x
- 1
) 2.
y -
1 =
-
1 −
3 (x -
6)
3. y
+ 2
= 2 −
3 (x -
9)
3
x +
y =
1
x +
3y =
9
2x -
3y =
24
4. y
+ 3
= -
(x -
5)
5. y
- 4
= 5 −
3 (x +
3)
6. y
+ 4
= -
2 −
5 (x -
1)
x
+ y
= 2
5
x -
3y =
-27
2
x +
5y =
-18
Wri
te e
ach
eq
uat
ion
in
slo
pe-
inte
rcep
t fo
rm.
7. y
+ 4
= 4
(x -
2)
8. y
- 5
= 1
−
3 (x -
6)
9. y
- 8
= -
1 −
4 (x +
8)
y
= 4
x -
12
y =
1 −
3 x +
3
y =
-
1 −
4 x +
6
10. y
- 6
= 3
(x -
1 −
3 ) 11
. y +
4 =
-2(
x +
5)
12. y
+ 5 −
3 = 1 −
2 (x -
2)
y
= 3
x +
5
y =
-2x
- 1
4 y
= 1 −
2 x -
8 −
3
Exam
ple
1Ex
amp
le 2
4-3
013_
023_
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 4-3
Cha
pte
r 4
19
Gle
ncoe
Alg
ebra
1
Skill
s Pr
acti
ceW
riti
ng
Eq
uati
on
s i
n P
oin
t-S
lop
e F
orm
Wri
te a
n e
qu
atio
n i
n p
oin
t-sl
ope
form
for
th
e li
ne
that
pas
ses
thro
ugh
eac
h p
oin
t w
ith
th
e gi
ven
slo
pe.
1.
( –1,
–2)
x
y
O
m =
3
2.
( 1, –
2)x
y O
m =
–1
3.
( 2, –
3)
x
y O
m =
0
y
+ 2
= 3
(x +
1)
y +
2 =
-(x
- 1
) y
+ 3
= 0
4. (
3, 1
), m
= 0
5.
(-
4, 6
), m
= 8
6.
(1,
-3)
, m =
-4
y
- 1
= 0
y
- 6
= 8
(x +
4)
y +
3 =
-4(
x -
1)
7. (
4, -
6), m
= 1
8.
(3,
3),
m =
4 −
3 9.
(-
5, -
1), m
= -
5 −
4
y
+ 6
= x
- 4
y
- 3
= 4 −
3 (x -
3)
y +
1 =
-
5 −
4 (x +
5)
Wri
te e
ach
eq
uat
ion
in
sta
nd
ard
for
m.
10. y
+ 1
= x
+ 2
11
. y +
9 =
-3(
x -
2)
12. y
- 7
= 4
(x +
4)
x
- y
= -
1 3
x +
y =
-3
4x -
y =
-23
13. y
- 4
= -
(x -
1)
14. y
- 6
= 4
(x +
3)
15. y
+ 5
= -
5(x
- 3
)
x
+ y
= 5
4
x -
y =
-18
5
x +
y =
10
16. y
- 1
0 =
-2(
x -
3)
17. y
- 2
= -
1 −
2 (x -
4)
18. y
+ 1
1 =
1 −
3 (x +
3)
2
x +
y =
16
x +
2y =
8
x -
3y =
30
Wri
te e
ach
eq
uat
ion
in
slo
pe-
inte
rcep
t fo
rm.
19. y
- 4
= 3
(x -
2)
20. y
+ 2
= -
(x +
4)
21. y
- 6
= -
2(x
+ 2
)
y
= 3
x -
2
y =
-x -
6
y =
-2x
+ 2
22. y
+ 1
= -
5(x
- 3
) 23
. y -
3 =
6(x
- 1
) 24
. y -
8 =
3(x
+ 5
)
y
= -
5x +
14
y =
6x -
3
y =
3x +
23
25. y
- 2
= 1 −
2 (x +
6)
26. y
+ 1
= -
1 −
3 (x +
9)
27. y
- 1 −
2 = x
+ 1 −
2
y
= 1 −
2 x +
5
y =
-
1 −
3 x -
4
y =
x +
1
4-3
013_
023_
ALG
1_A
_CR
M_C
04_C
R_6
6049
9.in
dd
1912
/21/
10
12:4
6 A
M
Answers (Lesson 4-3)
A01-A12_ALG1_A_CRM_C04_AN_660499.indd A8A01-A12_ALG1_A_CRM_C04_AN_660499.indd A8 12/21/10 1:24 AM12/21/10 1:24 AM
Co
pyr
ight
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lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 4 A9 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 4
20
Gle
ncoe
Alg
ebra
1
Prac
tice
Wri
tin
g E
qu
ati
on
s i
n P
oin
t-S
lop
e F
orm
Wri
te a
n e
qu
atio
n i
n p
oin
t-sl
ope
form
for
th
e li
ne
that
pas
ses
thro
ugh
eac
h p
oin
t w
ith
th
e gi
ven
slo
pe.
1. (
2, 2
), m
= -
3 2.
(1,
-6)
, m =
-1
3. (
-3,
-4)
, m =
0
y
- 2
= -
3(x -
2)
y +
6 =
-(x
- 1
) y
+ 4
= 0
4. (
1, 3
), m
= -
3 −
4 5.
(-
8, 5
), m
= -
2 −
5 6.
(3,
-3)
, m =
1 −
3
y
- 3
= -
3 −
4 (x -
1)
y -
5 =
-
2 −
5 (x +
8)
y +
3 =
1 −
3 (x -
3)
Wri
te e
ach
eq
uat
ion
in
sta
nd
ard
for
m.
7. y
- 1
1 =
3(x
- 2
) 8.
y -
10
= -
(x -
2)
9. y
+ 7
= 2
(x +
5)
3
x -
y =
-5
x +
y =
12
2x -
y =
-3
10. y
- 5
= 3 −
2 (x +
4)
11. y
+ 2
= -
3 −
4 (x +
1)
12. y
- 6
= 4 −
3 (x -
3)
3
x -
2y =
-22
3
x +
4y =
-11
4
x -
3y =
-6
13. y
+ 4
= 1
.5(x
+ 2
) 14
. y -
3 =
-2.
4(x
- 5
) 15
. y -
4 =
2.5
(x +
3)
3
x -
2y =
2
12x
+ 5
y =
75
5x -
2y =
-23
Wri
te e
ach
eq
uat
ion
in
slo
pe-
inte
rcep
t fo
rm.
16. y
+ 2
= 4
(x +
2)
17. y
+ 1
= -
7(x
+ 1
) 18
. y -
3 =
-5(
x +
12)
y
= 4
x +
6
y =
-7x
- 8
y
= -
5x -
57
19. y
- 5
= 3 −
2 (x +
4)
20. y
- 1 −
4 = -
3 (
x +
1 −
4 ) 21
. y -
2 −
3 = -
2 (x
- 1 −
4 )
y
= 3 −
2 x +
11
y =
-3x
- 1 −
2 y
= -
2x +
7 −
6
22. C
ON
STR
UC
TIO
N A
con
stru
ctio
n c
ompa
ny
char
ges
$15
per
hou
r fo
r de
bris
rem
oval
, pl
us
a on
e-ti
me
fee
for
the
use
of
a tr
ash
du
mps
ter.
Th
e to
tal
fee
for
9 h
ours
of
serv
ice
is $
195.
a. W
rite
th
e po
int-
slop
e fo
rm o
f an
equ
atio
n t
o fi
nd
the
tota
l fe
e y
for
any
nu
mbe
r of
h
ours
x.
b.
Wri
te t
he
equ
atio
n i
n s
lope
-in
terc
ept
form
. y =
15x
+ 6
0
c. W
hat
is
the
fee
for
the
use
of
a tr
ash
du
mps
ter?
$60
23. M
OV
ING
Th
ere
is a
dai
ly f
ee f
or r
enti
ng
a m
ovin
g tr
uck
, plu
s a
char
ge o
f $0
.50
per
mil
e dr
iven
. It
cost
s $6
4 to
ren
t th
e tr
uck
on
a d
ay w
hen
it
is d
rive
n 4
8 m
iles
.
a. W
rite
th
e po
int-
slop
e fo
rm o
f an
equ
atio
n t
o fi
nd
the
tota
l ch
arge
y f
or a
on
e-da
y re
nta
l w
ith
x m
iles
dri
ven
.
b.
Wri
te t
he
equ
atio
n i
n s
lope
-in
terc
ept
form
.
c. W
hat
is
the
dail
y fe
e? $
40
y -
195
= 1
5(x -
9)
y -
64
= 0
.5(x
- 4
8)
y =
0.5
x +
40
4-3
013_
023_
ALG
1_A
_CR
M_C
04_C
R_6
6049
9.in
dd
2012
/21/
10
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6 A
M
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 4-3
Cha
pte
r 4
21
Gle
ncoe
Alg
ebra
1
1.B
ICY
CLI
NG
Har
vey
ride
s h
is b
ike
at a
n
aver
age
spee
d of
12
mil
es p
er h
our.
In
oth
er w
ords
, he
ride
s 12
mil
es i
n 1
hou
r, 24
mil
es i
n 2
hou
rs, a
nd
so o
n. L
et h
be
the
nu
mbe
r of
hou
rs h
e ri
des
and
d b
e di
stan
ce t
rave
led.
Wri
te a
n e
quat
ion
for
th
e re
lati
onsh
ip b
etw
een
dis
tan
ce a
nd
tim
e in
poi
nt-
slop
e fo
rm.
d
- 1
2 =
12(
h -
1)
2. G
EOM
ETRY
Th
e pe
rim
eter
of
a sq
uar
e va
ries
dir
ectl
y w
ith
its
sid
e le
ngt
h. T
he
poin
t-sl
ope
form
of
the
equ
atio
n f
or t
his
fu
nct
ion
is
y -
4 =
4(x
- 1
). W
rite
th
e eq
uat
ion
in
sta
nda
rd f
orm
.
4
x -
y =
0
3.N
ATU
RE
Th
e fr
equ
ency
of
a m
ale
cric
ket’s
ch
irp
is r
elat
ed t
o th
e ou
tdoo
r te
mpe
ratu
re. T
he
rela
tion
ship
is
expr
esse
d by
th
e eq
uat
ion
T =
n +
40,
w
her
e T
is
the
tem
pera
ture
in
deg
rees
Fa
hre
nh
eit
and
n i
s th
e n
um
ber
of c
hir
ps
the
cric
ket
mak
es i
n 1
4 se
con
ds. U
se
the
info
rmat
ion
fro
m t
he
grap
h b
elow
to
wri
te a
n e
quat
ion
for
th
e li
ne
in p
oin
t-sl
ope
form
.
N
um
ber
of
Ch
irp
s15
105
025
20
y
x30
35
Temperature (°F)
3040 20 105070 60
S
amp
le a
nsw
er:
T -
60
= 1
(n -
20)
4.C
AN
OEI
NG
Geo
ff p
addl
es h
is c
anoe
at
an a
vera
ge s
peed
of
3.5
mil
es p
er h
our.
Aft
er 5
hou
rs o
f ca
noe
ing,
Geo
ff h
as
trav
eled
18
mil
es. W
rite
an
equ
atio
n i
n
poin
t-sl
ope
form
to
fin
d th
e to
tal
dist
ance
y
for
any
nu
mbe
r of
hou
rs x
.
y -
18
= 3
.5(x
- 5
)
5. A
VIA
TIO
N A
jet
plan
e ta
kes
off
and
con
sist
entl
y cl
imbs
20
feet
for
eve
ry
40 f
eet
it m
oves
hor
izon
tall
y. T
he
grap
h
show
s th
e tr
ajec
tory
of
the
jet.
Ho
rizo
nta
l Dis
tan
ce (
ft)
500
010
0015
0020
0025
00
Height (ft)
600
800
400
200
1000
1400
1200
a. W
rite
an
equ
atio
n i
n p
oin
t-sl
ope
form
fo
r th
e li
ne
repr
esen
tin
g th
e je
t’s
traj
ecto
ry.
y -
0 =
0.5
(x -
0)
b.
Wri
te t
he
equ
atio
n f
rom
par
t a
in
slop
e -i
nte
rcep
t fo
rm.
c. W
rite
th
e eq
uat
ion
in
sta
nda
rd f
orm
. x
- 2
y =
0
Wor
d Pr
oble
m P
ract
ice
Wri
tin
g E
qu
ati
on
s i
n P
oin
t-S
lop
e F
orm
y =
0.5
x
4-3
013_
023_
ALG
1_A
_CR
M_C
04_C
R_6
6049
9.in
dd
2112
/21/
10
12:4
6 A
M
Answers (Lesson 4-3)
A01-A12_ALG1_A_CRM_C04_AN_660499.indd A9A01-A12_ALG1_A_CRM_C04_AN_660499.indd A9 12/21/10 1:24 AM12/21/10 1:24 AM
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 4 A10 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 4
22
Gle
ncoe
Alg
ebra
1
Enri
chm
ent
x
y O
x
y
O
Co
llin
eari
ty
You
hav
e le
arn
ed h
ow t
o fi
nd
the
slop
e be
twee
n t
wo
poin
ts o
n a
lin
e. D
oes
it m
atte
r w
hic
h t
wo
poin
ts y
ou u
se?
How
doe
s yo
ur
choi
ce o
f po
ints
aff
ect
the
slop
e-in
terc
ept
form
of
the
equ
atio
n o
f th
e li
ne?
1. C
hoo
se t
hre
e di
ffer
ent
pair
s of
poi
nts
fro
m t
he
grap
h a
t th
e
righ
t. W
rite
th
e sl
ope-
inte
rcep
t fo
rm o
f th
e li
ne
usi
ng
each
pai
r.
y
= x
+ 1
2. H
ow a
re t
he
equ
atio
ns
rela
ted?
T
hey
are
th
e sa
me.
3. W
hat
con
clu
sion
can
you
dra
w f
rom
you
r an
swer
s to
Exe
rcis
es 1
an
d 2?
T
he
equ
atio
n o
f a
line
is t
he
sam
e n
o m
atte
r w
hic
h t
wo
po
ints
yo
u c
ho
ose
.
Wh
en p
oin
ts a
re c
onta
ined
in
th
e sa
me
lin
e, t
hey
are
sai
d to
be
coll
inea
r.
Eve
n th
ough
poi
nts
may
loo
k li
ke t
hey
form
a l
ine
whe
n co
nnec
ted,
it
does
not
mea
n t
hat
th
ey a
ctu
ally
do.
By
chec
kin
g pa
irs
of p
oin
ts o
n a
gra
ph
you
can
det
erm
ine
wh
eth
er t
he
grap
h r
epre
sen
ts a
lin
ear
rela
tion
ship
.
4. C
hoo
se s
ever
al p
airs
of
poin
ts f
rom
th
e gr
aph
at
the
righ
t an
d w
rite
th
e sl
ope-
inte
rcep
t fo
rm o
f th
e li
ne
con
tain
ing
each
pai
r.
S
amp
le a
nsw
er:
y =
x;
y =
2x -
2;
y =
2x +
1
5. W
hat
con
clu
sion
can
you
dra
w f
rom
you
r eq
uat
ion
s in
E
xerc
ise
4? I
s th
is a
lin
e?
T
he
po
ints
are
no
t co
llin
ear.
Th
is is
no
t a
line.
4-3
013_
023_
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10
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6 A
M
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 4-3
Cha
pte
r 4
23
Gle
ncoe
Alg
ebra
1
Gra
phin
g Ca
lcul
ator
Act
ivit
yW
riti
ng
Lin
ear
Eq
uati
on
s
Lis
ts c
an b
e u
sed
wit
h t
he
lin
ear
regr
essi
on f
un
ctio
n t
o w
rite
an
d ve
rify
li
nea
r eq
uat
ion
s gi
ven
tw
o po
ints
on
a l
ine,
or
the
slop
e of
a l
ine
and
a po
int
thro
ugh
wh
ich
it
pass
es. T
he
lin
ear
regr
essi
on f
un
ctio
n, L
inR
eg (
ax +
b),
is
fou
nd
un
der
the
ST
AT
CA
LC
men
u.
W
rite
th
e sl
ope-
inte
rcep
t fo
rm o
f an
eq
uat
ion
of
the
lin
e th
at p
asse
s th
rou
gh (
3, -
2) a
nd
(6,
4).
En
ter
the
x-co
ordi
nat
es o
f th
e po
ints
in
to L
1 an
d th
e y-
coor
din
ates
in
to L
2. U
se t
he
lin
ear
regr
essi
on f
un
ctio
n t
o w
rite
th
e eq
uat
ion
of
the
lin
e.
Key
stro
kes:
S
TA
T E
NT
ER
3 E
NT
ER
6 E
NT
ER
(
–) 2
EN
TE
R 4
E
NT
ER
S
TA
T
4
2nd
[L
1]
,
2nd
[L
2] E
NT
ER
.T
he
equ
atio
n i
s y
= 2
x -
8.
If y
ou h
ave
alre
ady
wri
tten
th
e eq
uat
ion
of
a li
ne,
you
can
use
th
e gi
ven
in
form
atio
n t
o ve
rify
you
r eq
uat
ion
.
Exer
cise
sW
rite
th
e sl
ope-
inte
rcep
t fo
rm a
nd
th
e st
and
ard
for
m o
f an
eq
uat
ion
of
the
lin
e th
at s
atis
fies
eac
h c
ond
itio
n.
1. p
asse
s th
roug
h (0
, 7)
and
( 1 −
7 ,
-5 )
2.
pas
ses
thro
ugh
(-5,
1),
(10,
10)
, and
(-
10, -
2)
y
= -
84x +
7;
84x +
y =
7
y =
3 −
5 x +
4;
3x -
5y =
- 2
0
3. p
asse
s th
rou
gh (
6, -
4), m
= 2 −
3
4. p
asse
s th
rou
gh (
3, 5
), m
= -
4
y
= 2 −
3 x -
8;
2x -
3y =
24
y =
-4x
+ 1
7; 4
x +
y =
17
5. x
-in
terc
ept:
1, y
-in
terc
ept:
- 1 −
2
6. p
asse
s th
rou
gh (
-18
, 11)
, y-i
nte
rcep
t: 3
y
= 1 −
2 x -
1 −
2 ; x -
2y =
1
y =
- 4 −
9 x +
3;
4x +
9y =
27
V
erif
y th
at t
he
equ
atio
n o
f th
e li
ne
pas
sin
g th
rou
gh (2
, -3)
wit
h s
lop
e -
3 −
4 c
an b
e w
ritt
en a
s 3x
+ 4
y =
-6.
Use
th
e gi
ven
poi
nt
and
slop
e to
det
erm
ine
a se
con
d po
int
thro
ugh
w
hic
h t
he
lin
e pa
sses
. En
ter
the
x-co
ordi
nat
es o
f th
e po
ints
in
to L
1 an
d th
e y-
coor
din
ates
in
to L
2. U
se L
inR
eg (
ax +
b)
to d
eter
min
e th
e sl
ope-
inte
rcep
t fo
rm o
f th
e eq
uat
ion
.
The
slo
pe-i
nter
cept
for
m o
f th
e eq
uati
on i
s y
= -
0.75
x -
1.5
or
y =
- 3 −
4 x
- 3 −
2 .
Th
is c
an b
e re
wri
tten
in
sta
nda
rd f
orm
as
3x +
4y
= -
6.
Exam
ple
1
Exam
ple
2
4-3
013_
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6 A
M
Answers (Lesson 4-3)
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Chapter 4 A11 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 4
24
Gle
ncoe
Alg
ebra
1
Stud
y G
uide
and
Inte
rven
tion
Para
llel
an
d P
erp
en
dic
ula
r Lin
es
Para
llel L
ines
Tw
o n
onve
rtic
al l
ines
are
par
alle
l if
th
ey h
ave
the
sam
e sl
ope.
All
ve
rtic
al l
ines
are
par
alle
l.
W
rite
an
eq
uat
ion
in
slo
pe-
inte
rcep
t fo
rm f
or t
he
lin
e th
at p
asse
s th
rou
gh (
-1,
6)
and
is
par
alle
l to
th
e gr
aph
of
y =
2x
+ 1
2.
A l
ine
para
llel
to
y =
2x
+ 1
2 h
as t
he
sam
e sl
ope,
2. R
epla
ce m
wit
h 2
an
d (x
1, y 1)
wit
h
(-1,
6)
in t
he
poin
t-sl
ope
form
.
y -
y1
= m
(x -
x1)
P
oin
t-slo
pe form
y
- 6
= 2
(x -
(-
1))
m =
2; (x
1,
y 1)
= (
-1,
6)
y
- 6
= 2
(x +
1)
Sim
plif
y.
y
- 6
= 2
x +
2
Dis
trib
utive
Pro
pert
y
y
= 2
x +
8
Slo
pe-inte
rcept
form
Th
eref
ore,
th
e eq
uat
ion
is
y =
2x
+ 8
.
Exer
cise
sW
rite
an
eq
uat
ion
in
slo
pe-
inte
rcep
t fo
rm f
or t
he
lin
e th
at p
asse
s th
rou
gh t
he
give
n p
oin
t an
d i
s p
aral
lel
to t
he
grap
h o
f ea
ch e
qu
atio
n.
1.
2.
3.
y
= x
- 4
y
= -
1 −
2 x +
3
y =
4 −
3 x +
7
4. (
-2,
2),
y =
4x
- 2
5.
(6,
4),
y =
1 −
3 x +
1
6. (
4, -
2), y
= -
2x +
3
y
= 4
x +
10
y =
1 −
3 x +
2
y =
-2x
+ 6
7. (
-2,
4),
y =
-3x
+ 1
0 8.
(-
1, 6
), 3x
+ y
= 1
2 9.
(4,
-6)
, x +
2y
= 5
y
= -
3x -
2
y =
-3x
+ 3
y
= -
1 −
2 x -
4
10. F
ind
an e
quat
ion
of
the
lin
e th
at h
as a
y-i
nte
rcep
t of
2 t
hat
is
para
llel
to
the
grap
h o
f th
e li
ne
4x +
2y
= 8
.
11. F
ind
an e
quat
ion
of
the
lin
e th
at h
as a
y-i
nte
rcep
t of
-1
that
is
para
llel
to
the
grap
h o
f th
e li
ne
x -
3y
= 6
.
12. F
ind
an e
quat
ion
of
the
lin
e th
at h
as a
y-i
nte
rcep
t of
-4
that
is
para
llel
to
the
grap
h o
f th
e li
ne
y =
6.
( –3,
3)
x
y
O
4x -
3y
= –
12
( -8,
7)
x
y
O
y =
- x
- 4
1 2
2
2
( 5, 1
)x
y
O
y =
x -
8
Exam
ple
y =
-2x
+ 2
y =
1 −
3 x -
1
y =
-4
4-4
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 4-4
Cha
pte
r 4
25
Gle
ncoe
Alg
ebra
1
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nu
ed)
Para
llel
an
d P
erp
en
dic
ula
r Lin
es
Perp
end
icu
lar
Lin
es T
wo
non
vert
ical
lin
es a
re p
erp
end
icu
lar
if t
hei
r sl
opes
are
n
egat
ive
reci
proc
als
of e
ach
oth
er. V
erti
cal
and
hor
izon
tal
lin
es a
re p
erpe
ndi
cula
r.
Wri
te a
n e
qu
atio
n i
n s
lop
e-in
terc
ept
form
for
th
e li
ne
that
pas
ses
thro
ugh
(-
4, 2
) an
d i
s p
erp
end
icu
lar
to t
he
grap
h o
f 2x
- 3
y =
9.
Fin
d th
e sl
ope
of 2
x -
3y
= 9
. 2
x -
3y
= 9
O
rigin
al equation
-3y
= -
2x +
9
Subtr
act
2x
from
each s
ide.
y =
2 −
3 x -
3
Div
ide e
ach s
ide b
y -
3.
Th
e sl
ope
of y
= 2 −
3 x -
3 i
s 2 −
3 . S
o, t
he
slop
e of
th
e li
ne
pass
ing
thro
ugh
(-
4, 2
) th
at i
s pe
rpen
dicu
lar
to t
his
lin
e is
th
e n
egat
ive
reci
proc
al o
f 2 −
3 , or
-
3 −
2 .U
se t
he
poin
t-sl
ope
form
to
fin
d th
e eq
uat
ion
.y
- y
1 =
m(x
- x
1)
Poin
t-slo
pe form
y -
2 =
-
3 −
2 (x -
(-
4))
m =
-
3
−
2 ;
(x1,
y 1)
= (
-4,
2)
y -
2 =
-
3 −
2 (x +
4)
Sim
plif
y.
y
- 2
= -
3 −
2 x -
6
Dis
trib
utive
Pro
pert
y
y
= -
3 −
2 x -
4
Slo
pe-inte
rcept
form
Exer
cise
s 1
. AR
CH
ITEC
TUR
E O
n t
he
arch
itec
t’s p
lan
s fo
r a
new
hig
h s
choo
l, a
wal
l re
pres
ente
d by
−−
−
M
N h
as e
ndp
oin
ts M
(-3,
-1
) a
nd
N
(2,
1). A
wal
l re
pres
ente
d by
−−
−
P
Q h
as e
ndp
oin
ts
P(4
, -4)
an
d Q
(-2,
11)
. Are
th
e w
alls
per
pen
dicu
lar?
Exp
lain
.
Y
es, b
ecau
se t
he
slo
pe
of
−−
M
N (
2 −
5 ) is
th
e n
egat
ive
reci
pro
cal o
f th
e sl
op
e
of
−−
P
Q (
- 5 −
2 ) .
Det
erm
ine
wh
eth
er t
he
grap
hs
of t
he
foll
owin
g eq
uat
ion
s ar
e p
ara
llel
or
per
pen
dic
ula
r.
2. 2
x +
y
= -
7, x
- 2y
= -
4, 4x
- y
= 5
fi
rst
two
are
per
pen
dic
ula
r
3. y
= 3x,
6x
- 2y
= 7
, 3y
= 9x
- 1
al
l are
par
alle
l
Wri
te a
n e
qu
atio
n i
n s
lop
e-in
terc
ept
form
for
th
e li
ne
that
pas
ses
thro
ugh
th
e gi
ven
poi
nt
and
is
per
pen
dic
ula
r to
th
e gr
aph
of
each
eq
uat
ion
.
4. (
4, 2
), y
= 1 −
2 x +
1
5. (
2, -
3), y
= -
2 −
3 x +
4
6. (
6, 4
), y
= 7
x +
1
y
= -
2x +
10
y =
3 −
2 x -
6
y =
- 1 −
7 x +
34
−
7
7. (
-8,
-7)
, y =
-x
- 8
8.
(6,
-2)
, y =
-3x
- 6
9.
(-
5, -
1), y
= 5 −
2 x -
3
y
= x
+ 1
y
= 1 −
3 x -
4
y =
- 2 −
5 x -
3
Exam
ple
4-4
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Answers (Lesson 4-4)
A01-A12_ALG1_A_CRM_C04_AN_660499.indd A11A01-A12_ALG1_A_CRM_C04_AN_660499.indd A11 12/21/10 1:24 AM12/21/10 1:24 AM
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cGraw
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ivision o
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cGraw
-Hill C
om
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pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 4 A12 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 4
26
Gle
ncoe
Alg
ebra
1
Skill
s Pr
acti
ceP
ara
llel
an
d P
erp
en
dic
ula
r Lin
es
Wri
te a
n e
qu
atio
n i
n s
lop
e-in
terc
ept
form
for
th
e li
ne
that
pas
ses
thro
ugh
th
e gi
ven
poi
nt
and
is
par
alle
l to
th
e gr
aph
of
the
give
n e
qu
atio
n.
1.
2.
3.
y
= 2
x +
1
y =
-x
y =
1 −
2 x +
3
4. (
3, 2
), y
= 3
x +
4
5. (
-1,
-2)
, y =
-3x
+ 5
6.
(-
1, 1
), y
= x
- 4
y
= 3
x -
7
y =
-3x
- 5
y
= x
+ 2
7. (
1, -
3), y
= -
4x -
1
8. (
-4,
2),
y =
x +
3
9. (
-4,
3),
y =
1 −
2 x -
6
y
= -
4x +
1
y =
x +
6
y =
1 −
2 x +
5
10. R
AD
AR
On
a r
adar
scr
een
, a p
lan
e lo
cate
d at
A(-
2, 4
) is
fly
ing
tow
ard
B(4
, 3
).
An
oth
er p
lan
e, l
ocat
ed a
t C
(-
3, 1
), is
fly
ing
tow
ard
D(3,
0
). A
re t
he
plan
es’ p
ath
s pe
rpen
dicu
lar?
Exp
lain
.
N
o;
the
slo
pes
are
eq
ual
, mea
nin
g t
he
pat
hs
are
par
alle
l.
Det
erm
ine
wh
eth
er t
he
grap
hs
of t
he
foll
owin
g eq
uat
ion
s ar
e p
ara
llel
or
per
pen
dic
ula
r. E
xpla
in.
11.
y =
2 −
3 x +
3,
y
= 3 −
2 x, 2
x -
3y
= 8
fi
rst
an
d t
hir
d a
re p
aral
lel;
slo
pes
are
eq
ual
12.
y
= 4
x, x
+ 4
y =
12,
4x
+ y
= 1
fi
rst
an
d s
eco
nd
are
per
pen
dic
ula
r; s
lop
es a
re n
egat
ive
reci
pro
cals
Wri
te a
n e
qu
atio
n i
n s
lop
e-in
terc
ept
form
for
th
e li
ne
that
pas
ses
thro
ugh
th
e gi
ven
poi
nt
and
is
per
pen
dic
ula
r to
th
e gr
aph
of
the
give
n e
qu
atio
n.
13. (
-3,
-2)
, y =
x +
2
14. (
4, -
1), y
= 2
x -
4
15. (
-1,
-6)
, x +
3y
= 6
y
= -
x -
5
y =
- 1 −
2 x +
1
y =
3x -
3
16. (
-4,
5),
y =
-4x
- 1
17
. (-
2, 3
), y
=
1 −
4 x -
4
18. (
0, 0
), y
=
1 −
2 x -
1
y
= 1 −
4 x +
6
y =
-4x
- 5
y
= -
2x
( –2,
2)
x
y O
y =
1 2x
+ 1
( 1, –
1)
x
y
O
y =
–x
+ 3
( –2,
–3)
x
y O
y =
2x
- 1
4-4
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 4-4
Cha
pte
r 4
27
Gle
ncoe
Alg
ebra
1
Prac
tice
P
ara
llel
an
d P
erp
en
dic
ula
r Lin
es
Wri
te a
n e
qu
atio
n i
n s
lop
e-in
terc
ept
form
for
th
e li
ne
that
pas
ses
thro
ugh
th
e gi
ven
poi
nt
and
is
par
alle
l to
th
e gr
aph
of
the
give
n e
qu
atio
n.
1. (
3, 2
), y
= x
+ 5
2.
(-
2, 5
), y
= -
4x +
2
3. (
4, -
6), y
= -
3
−
4
x
+ 1
y
= x
- 1
y
= -
4x -
3
y =
-
3 −
4 x -
3
4. (
5, 4
), y
= 2 −
5 x -
2
5. (
12, 3
), y
= 4 −
3 x +
5
6. (
3, 1
), 2x
+ y
= 5
y
= 2 −
5 x +
2
y =
4 −
3 x -
13
y =
-2x
+ 7
7. (
-3,
4),
3y =
2x
- 3
8.
(-
1, -
2), 3
x -
y =
5
9. (
-8,
2),
5x -
4y
= 1
y
= 2 −
3 x +
6
y =
3x +
1
y =
5 −
4 x +
12
10. (
-1,
-4)
, 9x
+ 3
y =
8
11. (
-5,
6),
4x +
3y
= 1
12
. (3,
1),
2x +
5y
= 7
y
= -
3x -
7
y =
-
4 −
3 x -
2 −
3 y
= -
2 −
5 x +
11
−
5
Wri
te a
n e
qu
atio
n i
n s
lop
e-in
terc
ept
form
for
th
e li
ne
that
pas
ses
thro
ugh
th
e gi
ven
poi
nt
and
is
per
pen
dic
ula
r to
th
e gr
aph
of
the
give
n e
qu
atio
n.
13. (
-2,
-2)
, y =
-
1
−
3
x
+ 9
14
. (-
6, 5
), x
- y
= 5
15
. (-
4, -
3), 4
x +
y =
7
y
= 3
x +
4
y =
-x -
1
y =
1 −
4 x -
2
16. (
0, 1
), x
+ 5
y =
15
17. (
2, 4
), x
- 6
y =
2
18. (
-1,
-7)
, 3x
+ 1
2y =
-6
y
= 5
x +
1
y =
-6x
+ 1
6 y
= 4
x -
3
19. (
-4,
1),
4x +
7y
= 6
20
. (10
, 5),
5x +
4y
= 8
21
. (4,
-5)
, 2x
- 5
y =
-10
y
= 7 −
4 x +
8
y =
4 −
5 x -
3
y =
-
5 −
2 x +
5
22. (
1, 1
), 3x
+ 2
y =
-7
23. (
-6,
-5)
, 4x
+ 3
y =
-6
24. (
-3,
5),
5x -
6y
= 9
y
= 2 −
3 x +
1 −
3 y
= 3 −
4 x -
1 −
2 y
= -
6 −
5 x +
7 −
5
25. G
EOM
ETRY
Qu
adri
late
ral
AB
CD
has
dia
gon
als
−−
A
C a
nd
−−
−
B
D .
D
eter
min
e w
het
her
−−
A
C i
s pe
rpen
dicu
lar
to −
−−
B
D . E
xpla
in.
Y
es;
they
are
per
pen
dic
ula
r b
ecau
se t
hei
r sl
op
es a
re
7
an
d -
1 −
7 , w
hic
h a
re n
egat
ive
reci
pro
cals
.
26. G
EOM
ETRY
Tri
angl
e A
BC
has
ver
tice
s A
(0, 4
), B
(1, 2
), an
d C
(4, 6
). D
eter
min
e w
het
her
tr
ian
gle
AB
C i
s a
righ
t tr
ian
gle.
Exp
lain
.
Y
es;
sid
es −
−
A
B a
nd
−−
A
C a
re p
erp
end
icu
lar
bec
ause
th
eir
slo
pes
are
-2
and
1 −
2 , w
hic
h a
re n
egat
ive
reci
pro
cals
.
x
y O
A
D
C
B
4-4
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M
Answers (Lesson 4-4)
A01-A12_ALG1_A_CRM_C04_AN_660499.indd A12A01-A12_ALG1_A_CRM_C04_AN_660499.indd A12 12/21/10 1:24 AM12/21/10 1:24 AM
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ight
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-Hill
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ivis
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raw
-Hill
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mp
anie
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c.
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
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The
McG
raw
-Hill
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mp
anie
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c.
PDF Pass
Chapter 4 A13 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 4
28
Gle
ncoe
Alg
ebra
1
1.B
USI
NES
S B
rady
’s B
ooks
is
a re
tail
st
ore.
Th
e st
ore’
s av
erag
e da
ily
prof
its
y ar
e gi
ven
by
the
equ
atio
n y
= 2
x +
3
wh
ere
x is
th
e n
um
ber
of h
ours
ava
ilab
le
for
cust
omer
pu
rch
ases
. Bra
dy’s
add
s an
on
lin
e sh
oppi
ng
opti
on. W
rite
an
eq
uat
ion
in
slo
pe-i
nte
rcep
t fo
rm t
o sh
ow
a n
ew p
rofi
t li
ne
wit
h t
he
sam
e pr
ofit
ra
te c
onta
inin
g th
e po
int
(0, 1
2).
y =
2x +
12
2.A
RC
HIT
ECTU
RE
Th
e fr
ont
view
of
a h
ouse
is
draw
n o
n g
raph
pap
er. T
he
left
si
de o
f th
e ro
of o
f th
e h
ouse
is
repr
esen
ted
by t
he
equ
atio
n y
= x
. Th
e ro
ofli
nes
in
ters
ect
at a
rig
ht
angl
e an
d th
e pe
ak o
f th
e ro
of i
s re
pres
ente
d by
th
e po
int
(5, 5
). W
rite
th
e eq
uat
ion
in
slo
pe-
inte
rcep
t fo
rm f
or t
he
lin
e th
at c
reat
es
the
righ
t si
de o
f th
e ro
of.
y =
-x +
10
3. A
RC
HA
EOLO
GY
An
arc
hae
olog
ist
is
com
pari
ng
the
loca
tion
of
a je
wel
ed b
ox
she
just
fou
nd
to t
he
loca
tion
of
a br
ick
wal
l. T
he
wal
l ca
n b
e re
pres
ente
d by
th
e
equ
atio
n y
= -
5 −
3 x +
13.
Th
e bo
x is
loc
ated
at
the
poin
t (1
0, 9
). W
rite
an
eq
uat
ion
rep
rese
nti
ng
a li
ne
that
is
perp
endi
cula
r to
th
e w
all
and
that
pas
ses
thro
ugh
th
e lo
cati
on o
f th
e bo
x.
y
= 3 −
5 x +
3
4.G
EOM
ETRY
A p
aral
lelo
gram
is
crea
ted
by t
he
inte
rsec
tion
s of
th
e li
nes
x=
2,
x
= 6
, y =
1 −
2 x +
2, a
nd
anot
her
lin
e. F
ind
t
he
equ
atio
n o
f th
e fo
urt
h l
ine
nee
ded
to
com
plet
e th
e pa
rall
elog
ram
. Th
e li
ne
shou
ld p
ass
thro
ugh
(2,
0).
(H
int:
Ske
tch
a
grap
h t
o h
elp
you
see
th
e li
nes
.)
y =
1 −
2 x -
1
5. IN
TER
IOR
DES
IGN
Pam
ela
is p
lan
nin
g to
in
stal
l an
isl
and
in h
er k
itch
en.
Sh
e dr
aws
the
shap
e sh
e li
kes
by c
onn
ecti
ng
the
vert
ices
of
the
squ
are
tile
s on
her
ki
tch
en f
loor
. Sh
e re
cord
s th
e lo
cati
on o
f ea
ch c
orn
er i
n t
he
tabl
e.
a. H
ow m
any
pair
s of
par
alle
l si
des
are
ther
e in
th
e sh
ape
AB
CD
sh
e de
sign
ed?
Exp
lain
.
1 p
air:
−−
B
C a
nd
−−
A
D a
re p
aral
lel
bec
ause
th
eir
slo
pes
are
bo
th
0.5.
b.
How
man
y pa
irs
of p
erpe
ndi
cula
r si
des
are
ther
e in
th
e sh
ape
she
desi
gned
? E
xpla
in.
2
pai
rs:
−−
B
C ⊥
−−
A
B a
nd
−−
A
B ⊥
−−
A
D
bec
ause
−−
A
B h
as a
slo
pe
of
-2,
w
hic
h is
th
e o
pp
osi
te r
ecip
roca
l o
f th
e sl
op
es o
f −
−
B
C a
nd
−−
A
D , 0
.5.
c. W
hat
is
the
shap
e of
her
new
isl
and?
a
trap
ezo
id
Wor
d Pr
oble
m P
ract
ice
Para
llel
an
d P
erp
en
dic
ula
r Lin
es
y
xO
( 5, 5
)
Co
rner
Dis
tan
ce
fro
m W
est
Wal
l (ti
les)
Dis
tan
ce
fro
m S
ou
th
Wal
l (ti
les)
A5
4
B3
8
C7
10
D11
7
4-4
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M
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 4-4
Cha
pte
r 4
29
Gle
ncoe
Alg
ebra
1
Enri
chm
ent
Pen
cils o
f Lin
es
All
of
the
lin
es t
hat
pas
s th
rou
gh
a si
ngl
e po
int
in t
he
sam
e pl
ane
are
call
ed a
pen
cil o
f li
nes
.A
ll l
ines
wit
h t
he
sam
e sl
ope,
bu
t di
ffer
ent
inte
rcep
ts, a
re a
lso
call
ed a
“pe
nci
l,” a
pen
cil o
f p
aral
lel l
ines
.
Gra
ph
som
e of
th
e li
nes
in
eac
h p
enci
l.
1. A
pen
cil
of l
ines
th
rou
gh t
he
2.
A p
enci
l of
lin
es d
escr
ibed
by
po
int
(1, 3
) y
- 4
= m
(x -
2),
wh
ere
m i
s an
y re
al n
um
ber
3. A
pen
cil
of l
ines
par
alle
l to
th
e li
ne
4.
A p
enci
l of
lin
es d
escr
ibed
by
x
- 2
y =
7
y =
mx
+ 3
m -
2 ,
wh
ere
m i
s an
y re
al n
um
ber
x
y
Ox
y
O
x
y
Ox
y
O
4-4
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6 A
M
Answers (Lesson 4-4)
A13-A24_ALG1_A_CRM_C04_AN_660499.indd A13A13-A24_ALG1_A_CRM_C04_AN_660499.indd A13 12/21/10 1:24 AM12/21/10 1:24 AM
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pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF 2nd
Chapter 4 A14 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 4
30
Gle
ncoe
Alg
ebra
1
Stud
y G
uide
and
Inte
rven
tion
Scatt
er
Plo
ts a
nd
Lin
es o
f Fit
Inve
stig
ate
Rel
atio
nsh
ips
Usi
ng
Sca
tter
Plo
ts A
sca
tter
plo
t is
a g
raph
in
w
hic
h t
wo
sets
of
data
are
plo
tted
as
orde
red
pair
s in
a c
oord
inat
e pl
ane.
If
y in
crea
ses
as x
in
crea
ses,
th
ere
is a
pos
itiv
e co
rrel
atio
n b
etw
een
x a
nd
y. I
f y
decr
ease
s as
x i
ncr
ease
s,
ther
e is
a n
egat
ive
corr
elat
ion
bet
wee
n x
an
d y.
If
x an
d y
are
not
rel
ated
, th
ere
is n
o co
rrel
atio
n.
EA
RN
ING
S T
he
grap
h a
t th
e ri
ght
show
s th
e am
oun
t of
mon
ey C
arm
en e
arn
ed e
ach
w
eek
an
d t
he
amou
nt
she
dep
osit
ed i
n h
er s
avin
gs
acco
un
t th
at s
ame
wee
k. D
eter
min
e w
het
her
th
e gr
aph
sh
ows
a p
osit
ive
corr
ela
tion
, a n
ega
tive
co
rrel
ati
on, o
r n
o co
rrel
ati
on. I
f th
ere
is a
p
osit
ive
or n
egat
ive
corr
elat
ion
, des
crib
e it
s m
ean
ing
in t
he
situ
atio
n.
Th
e gr
aph
sh
ows
a po
siti
ve c
orre
lati
on. T
he
mor
e C
arm
en e
arn
s, t
he
mor
e sh
e sa
ves.
Exer
cise
sD
eter
min
e w
het
her
eac
h g
rap
h s
how
s a
pos
itiv
e co
rrel
ati
on, a
neg
ati
ve
corr
ela
tion
, or
no
corr
ela
tion
. If
ther
e is
a p
osit
ive
or n
egat
ive
corr
elat
ion
, d
escr
ibe
its
mea
nin
g in
th
e si
tuat
ion
.
1.
2.
Neg
ativ
e co
rrel
atio
n;
as t
ime
incr
ease
s,
spee
d
dec
reas
es.
3.
4.
Ave
rage
Wee
kly
Wor
k H
ours
in U
.S.
Hours
34.0
34.2
33.8
33.6
34.4
34.6
Year
s Si
nce
1995
32
10
54
76
98
Sour
ce: T
he W
orld
Alm
anac
Ave
rage
Jogg
ing
Spee
d
Min
utes
Miles per Hour
010
205
1525
10 5
Carm
en’s
Ear
ning
s an
d Sa
ving
s
Dolla
rs E
arne
d
Dollars Saved
040
8012
0
35 30 25 20 15 10 5
no
co
rrel
atio
n
Exam
ple
Po
siti
ve
corr
elat
ion
; as
yea
rs
incr
ease
, th
e av
erag
e w
eekl
y w
ork
ho
urs
al
so
incr
ease
.
Po
siti
ve
corr
elat
ion
; as
yea
rs
incr
ease
, th
e am
ou
nt
of
imp
ort
s al
so
incr
ease
.
Ave
rage
U.S
. Hou
rly
Earn
ings
Hourly Earnings ($)
15 016171819
Year
s Si
nce
2003
Sour
ce: U
.S. D
ept.
of L
abor
12
34
5
U.S.
Impo
rts
from
Mex
ico
Imports ($ billions) 130 0
160
190
220
Year
s Si
nce
2003
Sour
ce: U
.S. C
ensu
s Bur
eau
12
34
5
4-5
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 4-5
Cha
pte
r 4
31
Gle
ncoe
Alg
ebra
1
Use
Lin
es o
f Fi
t
T
he
tab
le s
how
s th
e n
um
ber
of
stu
den
ts p
er c
omp
ute
r in
Eas
ton
H
igh
Sch
ool
for
cert
ain
sch
ool
year
s fr
om 1
996
to 2
008.
Year
19
96
19
98
20
00
20
02
20
04
20
06
20
08
Stu
den
ts p
er C
om
pu
ter
22
18
14
10
6.1
5.4
4.9
a. D
raw
a s
catt
er p
lot
and
det
erm
ine
w
hat
rel
atio
nsh
ip e
xist
s, i
f an
y.S
ince
y d
ecre
ases
as
x in
crea
ses,
th
e co
rrel
atio
n i
s n
egat
ive.
b.
Dra
w a
lin
e of
fit
for
th
e sc
atte
r p
lot.
Dra
w a
lin
e th
at p
asse
s cl
ose
to m
ost
of t
he
poin
ts.
A l
ine
of f
it i
s sh
own
.c.
Wri
te t
he
slop
e-in
terc
ept
form
of
an e
qu
atio
n
for
the
lin
e of
fit
.T
he
lin
e of
fit
sh
own
pas
ses
thro
ugh
(1
999,
16)
an
d (2
005,
5.7
). F
ind
the
slop
e.
m
=
5.7
- 1
6
−
20
05
-
19
99
m
= -
1.7
F
ind
b in
y =
-1.
7x +
b.
16
= -
1.7
· 1
993
+ b
34
04 =
b
Th
eref
ore,
an
equ
atio
n o
f a
lin
e of
fit
is
y =
-1.
7x +
340
4.
Exer
cise
sR
efer
to
the
tab
le f
or E
xerc
ises
1–3
.
1. D
raw
a s
catt
er p
lot.
2. D
raw
a l
ine
of f
it f
or t
he
data
.
3. W
rite
th
e sl
ope-
inte
rcep
tfo
rm o
f an
equ
atio
n f
or t
he
lin
e of
fit
.
T
he
po
ints
(0,
5.0
8)
and
(3,
5.8
1) g
ive
y =
0.2
43x +
5.0
8 as
a li
ne
of
fi t.
Mov
ie A
dmis
sion
Pri
ces
Admission ($)
5.4
5.6
5.2 5
5.86
6.2
Year
s Si
nce
1999
32
10
54
Sour
ce: U
.S. C
ensu
s B
urea
u
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nu
ed)
Scatt
er
Plo
ts a
nd
Lin
es o
f Fit
Stud
ents
per
Com
pute
rin
Eas
ton
Hig
h Sc
hool
Students per Computer
81216 4 02024
Year
1996
1998
2000
2002
2004
2006
2008
Exam
ple
Year
s S
ince
199
9A
dm
issi
on
(d
olla
rs)
0$
5.0
8
1$
5.3
9
2$
5.6
6
3$
5.8
1
4$
6.0
3
4-5
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M
Answers (Lesson 4-5)
A13-A24_ALG1_A_CRM_C04_AN_660499.indd A14A13-A24_ALG1_A_CRM_C04_AN_660499.indd A14 12/23/10 7:09 PM12/23/10 7:09 PM
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 4 A15 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 4
32
Gle
ncoe
Alg
ebra
1
Skill
s Pr
acti
ceS
catt
er
Plo
ts a
nd
Lin
es o
f Fit
Det
erm
ine
wh
eth
er e
ach
gra
ph
sh
ows
a p
osit
ive
corr
ela
tion
, a n
ega
tive
co
rrel
ati
on, o
r n
o co
rrel
ati
on. I
f th
ere
is a
pos
itiv
e or
neg
ativ
e co
rrel
atio
n,
des
crib
e it
s m
ean
ing
in t
he
situ
atio
n.
1.
2.
P
osi
tive
; th
e lo
ng
er t
he
exer
cise
, n
o c
orr
elat
ion
th
e m
ore
Cal
ori
es b
urn
ed.
3.
4.
N
egat
ive;
as
wei
gh
t in
crea
ses,
P
osi
tive
; as
th
e ye
ar in
crea
ses,
th
e n
um
ber
of
rep
etit
ion
s
th
e d
eale
rsh
ip’s
rev
enu
ed
ecre
ases
.
in
crea
ses
5. B
ASE
BA
LL T
he
scat
ter
plot
sh
ows
the
aver
age
pric
e of
a m
ajor
-lea
gue
base
ball
tic
ket
from
199
7 to
200
6.
a.
Det
erm
ine
wh
at r
elat
ion
ship
, if
any,
exi
sts
in t
he
data
. Exp
lain
. P
osi
tive
; as
th
e ye
ar
incr
ease
s, t
he
pri
ce in
crea
ses.
b.
Use
th
e po
ints
(19
98, 1
3.60
) an
d (2
003,
19.
00)
to w
rite
th
e sl
ope-
inte
rcep
t fo
rm o
f an
equ
atio
n f
or
the
lin
e of
fit
sh
own
in
th
e sc
atte
r pl
ot.
y =
1.0
8x -
214
4.24
c.
Pre
dict
th
e pr
ice
of a
tic
ket
in 2
009.
ab
ou
t $2
5.48
Wei
ght-
Lift
ing
Wei
ght (
poun
ds)
Repetitions
040
8020
6010
012
014
0
14 12 10 8 6 4 2
Libr
ary
Fine
s
Book
s Bo
rrow
ed
Fines (dollars)
02
45
67
89
13
10
7 6 5 4 3 2 1
Calo
ries
Bur
ned
Dur
ing
Exer
cise
Tim
e (m
inut
es)
Calories
020
4010
3050
60
600
500
400
300
200
100
Base
ball
Tick
et P
rice
s
Average Price ($)
1416 12 018202224
Year
’99
’98
’97
’01
’03
’00
Sour
ce: T
eam
Mar
ketin
g Re
port,
Chi
cago
’02
’04
’05
’06
Car
Dea
lers
hip
Reve
nue
Revenue(hundreds of thousands)
46 2 08101214
Year
’99
’01
’03
’00
’02
’04
’05
’06
’07
’08
4-5
024_
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 4-5
Cha
pte
r 4
33
Gle
ncoe
Alg
ebra
1
Prac
tice
S
catt
er
Plo
ts a
nd
Lin
es o
f Fit
Det
erm
ine
wh
eth
er e
ach
gra
ph
sh
ows
a p
osit
ive
corr
ela
tion
, a n
ega
tive
co
rrel
ati
on, o
r n
o co
rrel
ati
on. I
f th
ere
is a
pos
itiv
e or
neg
ativ
e co
rrel
atio
n,
des
crib
e it
s m
ean
ing
in t
he
situ
atio
n.
1.
2.
n
o c
orr
elat
ion
3. D
ISEA
SE T
he
tabl
e sh
ows
the
nu
mbe
r of
cas
es o
f F
oodb
orn
e B
otu
lism
in
th
e U
nit
ed S
tate
s fo
r th
e ye
ars
2001
to
2005
.
a.
Dra
w a
sca
tter
plo
t an
d de
term
ine
wh
at
rela
tion
ship
, if
any,
exi
sts
in t
he
data
.
Neg
ativ
e co
rrel
atio
n;
as t
he
year
in
crea
ses,
th
e n
um
ber
of
case
s d
ecre
ases
.
b. D
raw
a l
ine
of f
it f
or t
he
scat
ter
plot
.
Sam
ple
an
swer
giv
en.
c.
Wri
te t
he
slop
e-in
terc
ept
form
of
an e
quat
ion
for
th
e li
ne
of f
it.
Sam
ple
an
swer
: y =
-12
9.75
x +
906
4. Z
OO
S T
he
tabl
e sh
ows
the
aver
age
and
max
imu
m
lon
gevi
ty o
f va
riou
s an
imal
s in
cap
tivi
ty.
a. D
raw
a s
catt
er p
lot
and
dete
rmin
e w
hat
re
lati
onsh
ip, i
f an
y, e
xist
s in
th
e da
ta.
P
osi
tive
co
rrel
atio
n;
as t
he
aver
age
incr
ease
s, t
he
max
imu
m in
crea
ses.
b.
Dra
w a
lin
e of
fit
for
th
e sc
atte
r pl
ot.
Sam
ple
an
swer
: U
se (
15, 4
0), (
35, 7
0).
c. W
rite
th
e sl
ope-
inte
rcep
t fo
rm o
f an
equ
atio
n f
or t
he
lin
e of
fit
. S
amp
le a
nsw
er:
y =
1.5
x +
17.
5
d.
Pre
dict
th
e m
axim
um
lon
gevi
ty f
or a
n a
nim
al w
ith
an
ave
rage
lon
gevi
ty o
f 33
yea
rs.
abo
ut
67 y
r
Stat
e El
evat
ions
Mea
n El
evat
ion
(feet
)
Highest Point(thousands of feet)
1000
020
0030
00
16 12 8 4
Sour
ce: U
.S. G
eolo
gica
l Sur
vey
Tem
pera
ture
ver
sus
Rain
fall
Aver
age
Annu
al R
ainf
all (
inch
es)
AverageTemperature (ºF)
1015
2025
3035
4045
64 60 56 52 0
Sour
ce: N
atio
nal O
cean
ic a
nd A
tmos
pher
icAd
min
istr
atio
n
U.S.
Foo
dbor
neBo
tulis
m C
ases
Cases
2030 10 04050
Year
2001
2002
2003
2004
2005
Ani
mal
Lon
gevi
ty (Y
ears
)
Aver
age
Maximum
50
1015
2025
3035
4045
80 70 60 50 40 30 20 10
Sour
ce: C
ente
rs fo
r D
isea
se C
ontr
ol
U.S
. Fo
od
bo
rne
Bo
tulis
m C
ases
Year
20
01
20
02
20
03
20
04
20
05
Cas
es3
92
82
016
18
Sour
ce: W
alke
r’s M
amm
als
of t
he W
orld
Lo
ng
evit
y (y
ears
)
Avg
.12
25
15
83
54
04
12
0
Max
.4
75
04
02
07
07
76
15
4
Po
siti
ve;
as t
he
mea
n
elev
atio
n in
crea
ses,
th
e h
igh
est
po
int
incr
ease
s.
4-5
024_
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Answers (Lesson 4-5)
A13-A24_ALG1_A_CRM_C04_AN_660499.indd A15A13-A24_ALG1_A_CRM_C04_AN_660499.indd A15 12/21/10 1:24 AM12/21/10 1:24 AM
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 4 A16 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 4
34
Gle
ncoe
Alg
ebra
1
1.M
USI
C T
he
scat
ter
plot
sh
ows
the
nu
mbe
r of
CD
s in
mil
lion
s th
at w
ere
sold
fr
om 1
999
to 2
005.
If
the
tren
d co
nti
nu
ed, a
bou
t h
ow m
any
CD
s w
ere
sold
in
200
6?
Sam
ple
an
swer
: ar
ou
nd
70
0 m
illio
n
2. F
AM
ILY
Th
e ta
ble
show
s th
e pr
edic
ted
ann
ual
cos
t fo
r a
mid
dle
inco
me
fam
ily
to
rais
e a
chil
d fr
om b
irth
un
til
adu
lth
ood.
D
raw
a s
catt
er p
lot
and
desc
ribe
wh
at
rela
tion
ship
exi
sts
wit
hin
th
e da
ta.
T
her
e is
a p
osi
tive
co
rrel
atio
n
bet
wee
n t
he
child
’s a
ge
and
an
nu
al c
ost
.
3.H
OU
SIN
G T
he
med
ian
pri
ce o
f an
ex
isti
ng
hom
e w
as $
160,
000
in 2
000
and
$240
,000
in
200
7. I
f x
repr
esen
ts t
he
nu
mbe
r of
yea
rs s
ince
200
0, u
se t
hes
e da
ta p
oin
ts t
o de
term
ine
a li
ne
of b
est
fit
for
the
tren
ds i
n t
he
pric
e of
exi
stin
g h
omes
. Wri
te t
he
equ
atio
n i
n s
lope
-in
terc
ept
form
.
y
= 1
1,42
8.6x
+ 1
60,0
00
4.B
ASE
BA
LL T
he
tabl
e sh
ows
the
aver
age
len
gth
in
min
ute
s of
pro
fess
ion
al
base
ball
gam
es i
n s
elec
ted
year
s.
Sour
ce: E
lias
Spor
ts B
urea
u
a. D
raw
a s
catt
er p
lot
and
dete
rmin
e w
hat
rel
atio
nsh
ip, i
f an
y, e
xist
s in
th
e da
ta.
no
co
rrel
atio
n
b.
Exp
lain
wh
at t
he
scat
ter
plot
sh
ows.
Th
ere
is n
o c
on
sist
ent
tren
d
reg
ard
ing
th
e le
ng
th o
f g
ames
.
c. D
raw
a l
ine
of f
it f
or t
he
scat
ter
plot
.
See
lin
e o
f fi t
on
sca
tter
plo
t ab
ove.Time (min) 16
6 0
168
170
172
174
176
178
180
Year
’90
’92
’94
’96
’98
’00
’02
Ag
e (y
ears
)3
06
1215
y
x9
Annual Cost ($1000)
1112 10 91316 15 1417
Sou
rce:
The
Wor
ld A
lman
ac
Sou
rce:
RIA
A
Year
‘01
‘00
‘99
0‘0
3‘0
2‘0
5
y
x‘0
4
CDs (millions)
750
800
700
650
850
950
900W
ord
Prob
lem
Pra
ctic
eS
catt
er
Plo
ts a
nd
Lin
es o
f Fit
Co
st o
f R
aisi
ng
a C
hild
Bo
rn in
20
03
Ch
ild’s
A
ge
36
912
15
An
nu
al
Co
st (
$)10
,70
011
,70
012
,60
015
,00
016
,70
0
Ave
rag
e L
eng
th o
f M
ajo
r L
eag
ue
Bas
ebal
l Gam
es
Year
‘92
‘94
‘96
‘98
‘00
‘02
‘04
Tim
e (m
in)
17
0174
17
116
817
817
216
7
4-5
024_
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 4-5
Cha
pte
r 4
35
Gle
ncoe
Alg
ebra
1
Enri
chm
ent
Lati
tud
e a
nd
Tem
pera
ture
Th
e la
titu
de
of a
pla
ce o
n E
arth
is
th
e m
easu
re o
f it
s di
stan
ce f
rom
the
equ
ator
. Wh
at d
o yo
u t
hin
k is
th
e re
lati
onsh
ip b
etw
een
a c
ity’
s la
titu
de a
nd
its
mea
n J
anu
ary
tem
pera
ture
? A
t th
e ri
ght
is a
ta
ble
con
tain
ing
the
lati
tude
s an
d Ja
nu
ary
mea
n t
empe
ratu
res
for
fift
een
U.S
. cit
ies.
Sam
ple
an
swer
s ar
e g
iven
.
Sour
ces:
Nat
iona
l Wea
ther
Ser
vice
1. U
se t
he
info
rmat
ion
in
th
e ta
ble
to c
reat
e a
scat
ter
plot
an
d dr
aw a
lin
e of
bes
t fi
t fo
r th
e da
ta.
2. W
rite
an
equ
atio
n f
or t
he
lin
e of
fit
. Mak
e a
con
ject
ure
abo
ut
the
rela
tion
ship
be
twee
n a
cit
y’s
lati
tude
an
d it
s m
ean
Ja
nu
ary
tem
pera
ture
.
S
amp
le a
nsw
er:
y =
-2.
39x +
121
.86;
Th
e h
igh
er t
he
lati
tud
e, t
he
low
er t
he
tem
per
atu
re.
3. U
se y
our
equ
atio
n t
o pr
edic
t th
e Ja
nu
ary
mea
n t
empe
ratu
re o
f Ju
nea
u, A
lask
a, w
hic
h h
as l
atit
ude
58:
23 N
. -
17.7
º F
4. W
hat
wou
ld y
ou e
xpec
t to
be
the
lati
tude
of
a ci
ty w
ith
a J
anu
ary
mea
n t
empe
ratu
re
of 1
5°F
? 44
:42
N
5. W
as y
our
con
ject
ure
abo
ut
the
rela
tion
ship
bet
wee
n l
atit
ude
an
d te
mpe
ratu
re c
orre
ct?
Y
es;
as t
he
lati
tud
e in
crea
ses,
th
e te
mp
erat
ure
dec
reas
es.
6. R
esea
rch
th
e la
titu
des
and
tem
pera
ture
s fo
r ci
ties
in
th
e so
uth
ern
hem
isph
ere.
Doe
s yo
ur
con
ject
ure
hol
d fo
r th
ese
citi
es a
s w
ell?
Yes
.
Lati
tud
e (º
N)
Temperature (ºF)
70 60 50 40 30 20 10 0
-10T
L20
4060
1030
50
U.S
. Cit
yL
atitu
de
Jan
uar
y M
ean
Tem
per
atu
re
Alb
any,
New
Yo
rk4
2:4
0 N
20
.7°F
Alb
uq
ue
rqu
e,
New
Mexic
o3
5:0
7 N
34
.3°F
An
ch
ora
ge, A
laska
61
:11
N14
.9°F
Bir
min
gh
am
, A
lab
am
a3
3:3
2 N
41.
7°F
Ch
arl
esto
n,
So
uth
Ca
rolin
a3
2:4
7 N
47.
1°F
Ch
ica
go,
Illin
ois
41
:50
N2
1.0
°F
Co
lum
bu
s,
Oh
io3
9:5
9 N
26
.3°F
Du
luth
, M
inn
eso
ta4
6:4
7 N
7.0
°F
Fa
irb
an
ks, A
laska
64
:50
N-
10
.1°F
Ga
lve
sto
n, Texa
s2
9:1
4 N
52
.9°F
Ho
no
lulu
, H
aw
aii
21
:19
N7
2.9
°F
La
s V
ega
s,
Neva
da
36
:12
N4
5.1
°F
Mia
mi, F
lori
da
25
:47
N6
7.3
°F
Ric
hm
on
d, V
irg
inia
37
:32
N3
5.8
°F
Tu
cso
n, A
rizo
na
32
:12
N5
1.3
°F
4-5
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M
Answers (Lesson 4-5)
A13-A24_ALG1_A_CRM_C04_AN_660499.indd A16A13-A24_ALG1_A_CRM_C04_AN_660499.indd A16 12/21/10 1:24 AM12/21/10 1:24 AM
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 4 A17 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 4
36
Gle
ncoe
Alg
ebra
1
Exer
cise
sT
he
tab
le s
how
s th
e n
um
ber
of
mil
lion
s of
dol
lars
of
dir
ect
pol
itic
al c
ontr
ibu
tion
s re
ceiv
ed b
y D
emoc
rats
an
d R
epu
bli
can
sin
sel
ecte
d y
ears
.1.
Use
a s
prea
dsh
eet
to d
raw
a s
catt
er p
lot
and
a tr
endl
ine
for
the
data
. Let
x r
epre
sen
t th
e n
um
ber
of y
ears
sin
ce 1
990
and
let
y re
pres
ent
dire
ct p
olit
ical
con
trib
uti
ons
in m
illi
ons
of d
olla
rs.
See
stu
den
ts’ w
ork
.
2. P
redi
ct t
he
amou
nt
of d
irec
t po
liti
cal
con
trib
uti
ons
for
the
2010
ele
ctio
n.
Sam
ple
an
swer
: $1
169
mill
ion
or
$1.1
69 b
illio
n
Spre
adsh
eet
Act
ivit
yS
catt
er
Plo
ts
T
he
tab
le b
elow
sh
ows
the
nu
mb
er o
f m
etri
c to
ns
of g
old
pro
du
ced
in
min
es i
n t
he
Un
ited
Sta
tes
in s
elec
ted
yea
rs.
Use
a s
pre
adsh
eet
to d
raw
a s
catt
er p
lot
and
a t
ren
dli
ne
for
the
dat
a.
Let
x r
epre
sen
t th
e n
um
ber
of
year
s si
nce
200
0 an
d l
et y
rep
rese
nt
the
nu
mb
er o
f m
etri
c to
ns
of g
old
. Th
en p
red
ict
the
nu
mb
er o
f ou
nce
s of
go
ld p
rod
uce
d i
n 2
013.
Ste
p 1
U
se C
olu
mn
A f
or t
he
year
s si
nce
200
0 an
d C
olu
mn
B f
or t
he
nu
mbe
r of
met
ric
ton
s of
gol
d. T
o cr
eate
a g
raph
fro
m t
he
data
, sel
ect
the
data
in
Col
um
ns
A a
nd
B
and
choo
se C
har
t fr
om t
he
Inse
rt m
enu
. Sel
ect
an X
Y (
Sca
tter
) ch
art
to s
how
th
e da
ta p
oin
ts.
Ste
p 2
A
dd a
tre
ndl
ine
to t
he
grap
h b
y ch
oosi
ng
the
Ch
art
men
u. A
dd a
lin
ear
tren
dlin
e. U
se t
he
opti
ons
men
u t
o h
ave
the
tren
dlin
e fo
reca
st 5
yea
rs f
orw
ard.
U
sing
thi
s tr
endl
ine,
it
appe
ars
that
the
gol
d pr
oduc
tion
for
201
3 w
ill
be
appr
oxim
atel
y 15
0 m
etri
c to
ns.
A s
prea
dsh
eet
prog
ram
can
cre
ate
scat
ter
plot
s of
dat
a th
at y
ou e
nte
r. Yo
u c
an a
lso
hav
e th
e sp
read
shee
t gr
aph
a l
ine
of f
it, c
alle
d a
tren
dli
ne,
au
tom
atic
ally
.
Exam
ple
Sour
ce: O
pen
Secr
ets
Year
Co
ntr
ibu
tio
ns
19
90
28
1
19
94
33
7
19
98
44
5
20
02
717
20
06
10
85
Sour
ce: U
.S. G
eolo
gica
l Sur
vey
Yea
r 2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
Go
ld
353
335
298
277
247
256
252
238
233
210
4-5
A1
0 1 2 3 4 5 6 7 8 9
353
335
298
277
247
256
252
238
233
210
3 4 5 6 7 8 9 10 11 12 13 142
BC
DE
FG
H
15Sp
read
shee
t sa
mp
le
Sh
eet
1S
hee
t 2
Sh
eet
3
U.S.
Gol
d M
ine
Prod
uctio
n
Gold (metric tons)
100
150 50 0
200
250
300
350
400
Year
s si
nce
2000
510
15
036_
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M
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 4-6
Cha
pte
r 4
37
Gle
ncoe
Alg
ebra
1
Equ
atio
ns
of
Bes
t-Fi
t Li
nes
Man
y gr
aph
ing
calc
ula
tors
uti
lize
an
alg
orit
hm
cal
led
lin
ear
regr
essi
on t
o fi
nd
a pr
ecis
e li
ne
of f
it c
alle
d th
e b
est-
fit
lin
e. T
he
calc
ula
tor
com
pute
s th
e da
ta, w
rite
s an
equ
atio
n, a
nd
give
s yo
u t
he
corr
elat
ion
coe
ffic
ent,
a
mea
sure
of
how
clo
sely
th
e eq
uat
ion
mod
els
the
data
.
GA
S PR
ICES
Th
e ta
ble
sh
ows
the
pri
ce o
f a
gall
on o
f re
gula
r ga
soli
ne
at a
sta
tion
in
Los
An
gele
s, C
alif
orn
ia o
n J
anu
ary
1 of
var
iou
s ye
ars.
Year
20
05
20
06
20
07
20
08
20
09
2010
Ave
rag
e P
rice
$1.
47
$1.
82
$2
.15
$2
.49
$2
.83
$3
.04
Sour
ce: U
.S. D
epar
tmen
t of
Ene
rgy
a. U
se a
gra
ph
ing
calc
ula
tor
to w
rite
an
eq
uat
ion
for
th
e b
est-
fit
lin
e fo
r th
at d
ata.
En
ter
the
data
by
pres
sin
g S
TA
T
and
sele
ctin
g th
e E
dit
opti
on. L
et t
he
year
200
5 be
rep
rese
nte
d by
0. E
nte
r th
e ye
ars
sin
ce 2
005
into
Lis
t 1
(L1)
. En
ter
the
aver
age
pric
e in
to L
ist
2 (L
2).
Th
en, p
erfo
rm t
he
lin
ear
regr
essi
on b
y pr
essi
ng
ST
AT
an
d se
lect
ing
the
CA
LC
opt
ion
. Scr
oll
dow
n t
o L
inR
eg (
ax+
b) a
nd
pres
s E
NT
ER
. Th
e be
st-f
it e
quat
ion
for
th
e re
gres
sion
is
show
n
to b
e y
= 0
.321
x +
1.4
99.
b.
Nam
e th
e co
rrel
atio
n c
oeff
icie
nt.
Th
e co
rrel
atio
n c
oeff
icie
nt
is t
he
valu
e sh
own
for
r o
n t
he
calc
ula
tor
scre
en. T
he
corr
elat
ion
co
effi
cien
t is
abo
ut
0.99
8.
Exer
cise
sW
rite
an
eq
uat
ion
of
the
regr
essi
on l
ine
for
the
dat
a in
eac
h t
able
bel
ow. T
hen
fi
nd
th
e co
rrel
atio
n c
oeff
icie
nt.
1. O
LYM
PIC
S B
elow
is
a ta
ble
show
ing
the
nu
mbe
r of
gol
d m
edal
s w
on b
y th
e U
nit
ed
Sta
tes
at t
he
Win
ter
Oly
mpi
cs d
uri
ng
vari
ous
year
s.Ye
ar19
92
19
94
19
98
20
02
20
06
2010
Go
ld M
edal
s5
66
10
99
Sour
ce: I
nter
natio
nal O
lym
pic
Com
mitt
ee
L
et x
rep
rese
nt
year
s si
nce
199
2; y
= 0.
25x +
5.4
1; r
= 0
.843
2. I
NTE
RES
T R
ATE
S B
elow
is
a ta
ble
show
ing
the
U.S
. Fed
eral
Res
erve
’s p
rim
e in
tere
st
rate
on
Jan
uar
y 1
of v
ario
us
year
s.Ye
ar2
00
62
00
72
00
82
00
92
010
Pri
me
Rat
e (p
erce
nt)
7.2
58
.25
7.2
53
.25
3.2
5
Sour
ce: F
eder
al R
eser
ve B
oard
L
et x
rep
rese
nt
year
s si
nce
20
06;
y =
-
1.3x
+ 8
.45;
r =
-0.
853
Stud
y G
uide
and
Inte
rven
tion
Reg
ressio
n a
nd
Med
ian
-Fit
Lin
es
Exam
ple
4-6
036_
048_
ALG
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_CR
M_C
04_C
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10
12:4
7 A
M
Answers (Lesson 4-5 and Lesson 4-6)
A13-A24_ALG1_A_CRM_C04_AN_660499.indd A17A13-A24_ALG1_A_CRM_C04_AN_660499.indd A17 12/21/10 1:24 AM12/21/10 1:24 AM
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 4 A18 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 4
38
Gle
ncoe
Alg
ebra
1
Equ
atio
ns
of
Med
ian
-Fit
Lin
es A
gra
phin
g ca
lcu
lato
r ca
n a
lso
fin
d an
oth
er t
ype
of
best
-fit
lin
e ca
lled
th
e m
edia
n-f
it l
ine,
wh
ich
is
fou
nd
usi
ng
the
med
ian
s of
th
e co
ordi
nat
es
of t
he
data
poi
nts
. ELEC
TIO
NS
Th
e ta
ble
sh
ows
the
tota
l n
um
ber
of
peo
ple
in
mil
lion
s w
ho
vote
d i
n t
he
U.S
. Pre
sid
enti
al e
lect
ion
in
th
e gi
ven
yea
rs.
Year
19
80
19
84
19
88
19
92
19
96
20
04
2
00
8
Vote
rs8
6.5
92
.79
1.6
10
4.4
96
.312
2.3
13
1.3
Sour
ce: G
eorg
e M
ason
Uni
vers
ity
a. F
ind
an
eq
uat
ion
for
th
e m
edia
n-f
it l
ine.
En
ter
the
data
by
pres
sin
g S
TA
T a
nd
sele
ctin
g th
e E
dit
opti
on. L
et t
he
year
198
0 be
rep
rese
nte
d by
0. E
nte
r th
e ye
ars
sin
ce 1
980
into
Lis
t 1
(L1)
. E
nte
r th
e n
um
ber
of v
oter
s in
to L
ist
2 (L
2).
Th
en, p
ress
S
TA
T a
nd
sele
ct t
he
CA
LC
opt
ion
. Scr
oll
dow
n t
o M
ed-M
ed o
ptio
n a
nd
pres
s E
NT
ER
. Th
e va
lue
of a
is
the
slop
e,
and
the
valu
e of
b i
s th
e y-
inte
rcep
t.T
he
equ
atio
n f
or t
he
med
ian
-fit
lin
e is
y =
1.5
5x +
8
3.5
7.
b.
Est
imat
e th
e n
um
ber
of
peo
ple
wh
o vo
ted
in
th
e 20
00 U
.S.
Pre
sid
enti
al e
lect
ion
. Gra
ph t
he
best
-fit
lin
e. T
hen
use
th
e T
RA
CE
feat
ure
an
d th
e ar
row
key
s u
nti
l yo
u f
ind
a po
int
wh
ere
x =
20.
Wh
en x
= 2
0, y
≈ 1
15. T
her
efor
e, a
bou
t 11
5 m
illi
on p
eopl
e vo
ted
in t
he
2000
U.S
. P
resi
den
tial
ele
ctio
n.
Exer
cise
sW
rite
an
eq
uat
ion
of
the
regr
essi
on l
ine
for
the
dat
a in
eac
h t
able
bel
ow. T
hen
fi
nd
th
e co
rrel
atio
n c
oeff
icie
nt.
1. P
OPU
LATI
ON
GR
OW
TH B
elow
is
a ta
ble
show
ing
the
esti
mat
ed p
opu
lati
on o
f Ari
zon
a in
mil
lion
s on
Ju
ly 1
st o
f va
riou
s ye
ars.
Year
20
01
20
02
20
03
20
04
20
05
20
06
Po
pu
lati
on
5.3
05
.44
5.5
85
.74
5.9
46
.17
Sour
ce: U
.S. C
ensu
s B
urea
u
a. F
ind
an e
quat
ion
for
th
e m
edia
n-f
it l
ine.
y =
0.1
71x +
5.2
67b
. P
redi
ct t
he
popu
lati
on o
f Ari
zon
a in
200
9. a
bo
ut
6.63
mill
ion
2. E
NR
OLL
MEN
T B
elow
is
a ta
ble
show
ing
the
nu
mbe
r of
stu
den
ts e
nro
lled
at
Hap
py
Day
s P
resc
hoo
l in
th
e gi
ven
yea
rs.
Year
20
02
20
04
20
06
20
08
2010
Stu
den
ts13
016
818
42
01
23
4
a. F
ind
an e
quat
ion
for
th
e m
edia
n-f
it l
ine.
y =
11.
42x +
137
.83
b.
Est
imat
e h
ow m
any
stu
den
ts w
ere
enro
lled
in
200
7. a
bo
ut
195
stu
den
ts
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nu
ed)
Reg
ressio
n a
nd
Med
ian
-Fit
Lin
es
Exam
ple
4-6
036_
048_
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_CR
M_C
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R_6
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9.in
dd
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10
12:4
7 A
M
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 4-6
Cha
pte
r 4
39
Gle
ncoe
Alg
ebra
1
Wri
te a
n e
qu
atio
n o
f th
e re
gres
sion
lin
e fo
r th
e d
ata
in e
ach
tab
le b
elow
. Th
en
fin
d t
he
corr
elat
ion
coe
ffic
ien
t.
1. S
OC
CER
Th
e ta
ble
show
s th
e n
um
ber
of g
oals
a s
occe
r te
am s
core
d ea
ch s
easo
n
sin
ce 2
005.
y =
1.
31x +
44.
38;
r =
0.7
14Ye
ar2
00
52
00
62
00
72
00
82
00
92
010
Go
als
Sco
red
42
48
46
50
52
48
2. P
HY
SIC
AL
FITN
ESS
Th
e ta
ble
show
s th
e pe
rcen
tage
of
seve
nth
gra
de s
tude
nts
in
pu
blic
sch
ool
wh
o m
et a
ll s
ix o
f C
alif
orn
ia’s
ph
ysic
al f
itn
ess
stan
dard
s ea
ch y
ear
sin
ce 2
002.
y =
3.1
4x +
29.
06;
r =
0.7
59Ye
ar2
00
22
00
32
00
42
00
52
00
6
Per
cen
tag
e2
4.0
%3
6.4
%3
8.0
%4
0.8
%3
7.5
%
Sour
ce: C
alifo
rnia
Dep
artm
ent
of E
duca
tion
3. T
AX
ES T
he
tabl
e sh
ows
the
esti
mat
ed s
ales
tax
rev
enu
es, i
n b
illi
ons
of d
olla
rs, f
or
Mas
sach
use
tts
each
yea
r si
nce
200
4. y
= 0.
172x
+ 3
.712
; r
= 0
.979
Year
20
04
20
05
20
06
20
07
20
08
Tax
Rev
enu
e3
.75
3.8
94
.00
4.1
74
.47
Sour
ce: B
eaco
n H
ill In
stitu
te
4. P
UR
CH
ASI
NG
Th
e S
ure
Sav
e su
perm
arke
t ch
ain
clo
sely
mon
itor
s h
ow m
any
diap
ers
are
sold
eac
h y
ear
so t
hat
th
ey c
an r
easo
nab
ly p
redi
ct h
ow m
any
diap
ers
wil
l be
sol
d in
th
e fo
llow
ing
year
.
Year
20
06
20
07
20
08
20
09
2010
Dia
per
s S
old
60
,20
06
5,0
00
66
,30
06
5,2
00
70
,60
0
a. F
ind
an e
quat
ion
for
th
e m
edia
n-f
it l
ine.
y =
17
67x +
62,
067
b.
How
man
y di
aper
s sh
ould
Su
reS
ave
anti
cipa
te s
elli
ng
in 2
011?
ab
ou
t 70
,90
0
5. F
AR
MIN
G S
ome
crop
s, s
uch
as
barl
ey, a
re v
ery
sen
siti
ve t
o h
ow a
cidi
c th
e so
il i
s. T
o de
term
ine
the
idea
l le
vel
of a
cidi
ty, a
far
mer
mea
sure
d h
ow m
any
bush
els
of b
arle
y h
e h
arve
sts
in d
iffe
ren
t fi
elds
wit
h v
aryi
ng
acid
ity
leve
ls.
So
il A
cid
ity
(pH
)5
.76
.26
.66
.87.
1
Bu
shel
s H
arve
sted
32
04
86
17
3
a. F
ind
an e
quat
ion
for
th
e re
gres
sion
lin
e. y
= 5
2.7x
- 3
00;
r =
0.9
91
b.
Acc
ordi
ng
to t
he
equ
atio
n, h
ow m
any
bush
els
wou
ld t
he
farm
er h
arve
st i
f th
e so
il h
ad
a pH
of
10?
abo
ut
227
bush
els
c. I
s th
is a
rea
son
able
pre
dict
ion
? E
xpla
in.
No
, bec
ause
bar
ley
may
no
t g
row
w
ell a
t ve
ry la
rge
pH
val
ues
.
Skill
s Pr
acti
ceR
eg
ressio
n a
nd
Med
ian
-Fit
Lin
es
4-6
036_
048_
ALG
1_A
_CR
M_C
04_C
R_6
6049
9.in
dd
3912
/21/
10
12:4
7 A
M
Answers (Lesson 4-6)
A13-A24_ALG1_A_CRM_C04_AN_660499.indd A18A13-A24_ALG1_A_CRM_C04_AN_660499.indd A18 12/21/10 1:24 AM12/21/10 1:24 AM
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF 2nd
Chapter 4 A19 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 4
40
Gle
ncoe
Alg
ebra
1
Wri
te a
n e
qu
atio
n o
f th
e re
gres
sion
lin
e fo
r th
e d
ata
in e
ach
tab
le b
elow
. Th
en
fin
d t
he
corr
elat
ion
coe
ffic
ien
t.
1. T
UR
TLES
Th
e ta
ble
show
s th
e n
um
ber
of t
urt
les
hat
ched
at
a zo
o ea
ch y
ear
sin
ce 2
006.
Year
20
06
20
07
20
08
20
09
2010
Turt
les
Hat
ched
21
17
16
16
14
y
= –1.
5x +
19.
8; r
= -
0.91
6
2. S
CH
OO
L LU
NC
HES
Th
e ta
ble
show
s th
e pe
rcen
tage
of
stu
den
ts r
ecei
vin
g fr
ee o
r re
duce
d pr
ice
sch
ool
lun
ches
at
a ce
rtai
n s
choo
l ea
ch y
ear
sin
ce 2
006.
Year
20
06
20
07
20
08
20
09
2010
Per
cen
tag
e14
.4%
15
.8%
18
.3%
18
.6%
20
.9%
So
urce
: Kid
sDat
a
y
= 1.
58x +
14.
44;
r =
0.9
83
3. S
POR
TS B
elow
is
a ta
ble
show
ing
the
nu
mbe
r of
stu
den
ts s
ign
ed u
p to
pla
y la
cros
se
afte
r sc
hoo
l in
eac
h a
ge g
rou
p.
Ag
e13
14
15
16
17
Lac
ross
e P
laye
rs17
14
69
12
4. L
AN
GU
AG
E T
he
Sta
te o
f C
alif
orn
ia k
eeps
tra
ck o
f h
ow m
any
mil
lion
s of
stu
den
ts a
re
lear
nin
g E
ngl
ish
as
a se
con
d la
ngu
age
each
yea
r.
Year
20
03
20
04
20
05
20
06
20
07
En
glis
h L
earn
ers
1.6
00
1.5
99
1.5
92
1.5
70
1.5
69
Sour
ce: C
alifo
rnia
Dep
artm
ent
of E
duca
tion
a. F
ind
an e
quat
ion
for
th
e m
edia
n-f
it l
ine.
y =
-
0.01
x +
1.6
07
b.
Pre
dict
th
e n
um
ber
of s
tude
nts
wh
o w
ere
lear
nin
g E
ngl
ish
in
Cal
ifor
nia
in
200
1.
ab
ou
t 1,
627,
00
0 st
ud
ents
c. P
redi
ct t
he
nu
mbe
r of
stu
den
ts w
ho
wer
e le
arn
ing
En
glis
h i
n C
alif
orn
ia i
n 2
010.
abo
ut
1,53
7,0
00
stu
den
ts
5. P
OPU
LATI
ON
Det
roit
, Mic
hig
an, l
ike
a n
um
ber
of l
arge
cit
ies,
is
losi
ng
popu
lati
on
ever
y ye
ar. B
elow
is
a ta
ble
show
ing
the
popu
lati
on o
f D
etro
it e
ach
dec
ade.
Year
19
60
19
70
19
80
19
90
20
00
Po
pu
lati
on
(m
illio
ns)
1.6
71.
51
1.2
01.
03
0.9
5
Sour
ce: U
.S. C
ensu
s B
urea
u
a. F
ind
an e
quat
ion
for
th
e re
gres
sion
lin
e. y
= -
0.01
9x +
1.6
56
b.
Fin
d th
e co
rrel
atio
n c
oeff
icie
nt
and
expl
ain
th
e m
ean
ing
of i
ts s
ign
.r
= -
0.98
2; T
he
sig
n is
neg
ativ
e, m
ean
ing
th
at t
her
e is
a n
egat
ive
corr
elat
ion
to
th
e d
ata.
c. E
stim
ate
the
popu
lati
on o
f D
etro
it i
n 2
008.
ab
ou
t 73
4,0
00
peo
ple
Prac
tice
Reg
ressio
n a
nd
Med
ian
-Fit
Lin
es
y =
-
1.5x
+ 3
4.1;
r =
-0.
554
4-6
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6049
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4 P
M
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 4-6
4-6
Cha
pte
r 4
41
Gle
ncoe
Alg
ebra
1
Wor
d Pr
oble
m P
ract
ice
Reg
ressio
n a
nd
Med
ian
-Fit
Lin
es
1. F
OO
TBA
LL R
utg
ers
Un
iver
sity
ru
nn
ing
back
Ray
Ric
e ra
n f
or 1
732
tota
l ya
rds
in
the
2007
reg
ula
r se
ason
. Th
e ta
ble
belo
w
show
s h
is c
um
ula
tive
tot
al n
um
ber
of
yard
s ra
n a
fter
sel
ect
gam
es.
Gam
e N
um
ber
13
69
12
Cu
mu
lati
ve
Yard
s18
44
31
818
12
57
17
32
Sour
ce: R
utge
rs U
nive
rsity
Ath
letic
s
U
se a
cal
cula
tor
to f
ind
an e
quat
ion
for
th
e re
gres
sion
lin
e sh
owin
g th
e to
tal
yard
s y
scor
ed a
fter
x g
ames
. Wh
at i
s th
e re
al-w
orld
mea
nin
g of
th
e va
lue
retu
rned
for
a?
y
= 14
0.4x
+ 1
3.8;
a r
epre
sen
ts
the
nu
mb
er o
f ya
rds
Ray
Ric
e ca
n
be
exp
ecte
d t
o r
un
per
gam
e.
2. G
OLD
Ou
nce
s of
gol
d ar
e tr
aded
by
larg
e in
vest
men
t ba
nks
in
com
mod
ity
exch
ange
s m
uch
th
e sa
me
way
th
at
shar
es o
f st
ock
are
trad
ed. T
he
tabl
e be
low
sh
ows
the
cost
of
a si
ngl
e ou
nce
of
gold
on
th
e la
st d
ay o
f tr
adin
g in
giv
en
year
s.
Year
2002
2003
2004
2005
2006
Pri
ce
$346.7
0$414.8
0$438.1
0$517.
20
$636.3
0
Sour
ce: G
loba
l Fin
anci
al D
ata
U
se a
cal
cula
tor
to f
ind
an e
quat
ion
for
th
e re
gres
sion
lin
e. T
hen
pre
dict
th
e pr
ice
of a
n o
un
ce o
f go
ld o
n t
he
last
day
of
tra
din
g in
200
9. I
s th
is a
rea
son
able
pr
edic
tion
? E
xpla
in.
y
= 68
.16x
+ 3
34.3
; $8
11.4
2; T
he
pre
dic
tio
n m
ay n
ot
be
reas
on
able
, b
ecau
se t
he
valu
e o
f an
in
vest
men
t ca
n fl
uct
uat
e.
3. G
OLF
SC
OR
ES E
mm
anu
el i
s pr
acti
cin
g go
lf a
s pa
rt o
f h
is s
choo
l’s g
olf
team
. E
ach
wee
k h
e pl
ays
a fu
ll r
oun
d of
gol
f an
d re
cord
s h
is t
otal
sco
re. H
is s
core
card
af
ter
five
wee
ks i
s be
low
.W
eek
12
34
5
Go
lf S
core
112
10
710
810
49
8
U
se a
cal
cula
tor
to f
ind
an e
quat
ion
for
th
e m
edia
n-f
it l
ine.
Th
en e
stim
ate
how
m
any
gam
es E
mm
anu
el w
ill
hav
e to
pla
y to
get
a s
core
of
86.
y
= -
2.83
x +
114
.67;
ab
ou
t 10
g
ames
4. S
TUD
ENT
ELEC
TIO
NS
Th
e vo
te t
otal
s fo
r fi
ve o
f th
e ca
ndi
date
s pa
rtic
ipat
ing
in
Mon
tval
e H
igh
Sch
ool’s
stu
den
t co
un
cil
elec
tion
s an
d th
e n
um
ber
of h
ours
eac
h
can
dida
te s
pen
t ca
mpa
ign
ing
are
show
n
in t
he
tabl
e be
low
.
Ho
urs
C
amp
aig
nin
g1
34
68
Vote
s R
ecei
ved
92
22
44
67
8
a. U
se a
cal
cula
tor
to f
ind
an e
quat
ion
fo
r th
e m
edia
n-f
it l
ine.
y =
9.
3x -
6.4
7
b.
Plo
t th
e da
ta p
oin
ts a
nd
draw
th
e m
edia
n-f
it l
ine
on t
he
grap
h b
elow
.
Votes Received
2030 10 04050607080
Cam
paig
n Ti
me
(h)
32
15
74
68
x
y
c. S
upp
ose
a si
xth
can
dida
te s
pen
ds
7 h
ours
cam
paig
nin
g. E
stim
ate
how
m
any
vote
s th
at c
andi
date
cou
ld
expe
ct t
o re
ceiv
e. a
bo
ut
59
4-6
036_
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2:30
PM
Answers (Lesson 4-6)
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-Hill C
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ht © G
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ivision o
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-Hill C
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PDF Pass
Chapter 4 A20 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 4
42
Gle
ncoe
Alg
ebra
1
For
som
e se
ts o
f da
ta, a
lin
ear
equ
atio
n i
n t
he
form
y =
ax
+ b
doe
s n
ot a
dequ
atel
y de
scri
be
the
rela
tion
ship
bet
wee
n d
ata
poin
ts. T
he
“Qu
adR
eg”
fun
ctio
n o
n a
gra
phin
g ca
lcu
lato
r w
ill
outp
ut
an e
quat
ion
in
th
e fo
rm y
= a
x2 +
bx
+ c
. Th
e va
lue
of R
2 , th
e co
effi
cien
t of
d
eter
min
atio
n t
ells
you
how
clo
sely
th
e pa
rabo
la f
its
the
data
.
T
he
tab
le s
how
s th
e p
opu
lati
on o
f A
tlan
ta i
n v
ario
us
year
s.
Year
19
70
19
80
19
90
20
00
20
05
20
07
Po
pu
lati
on
49
7,0
00
42
5,0
00
39
4,0
17
416
,474
47
0,6
88
49
8,1
09
Sour
ce: U
.S. C
ensu
s B
urea
u
a. F
ind
th
e eq
uat
ion
of
a q
uad
rati
c-re
gres
sion
par
abol
a fo
r th
e d
ata.
Ru
nn
ing
a li
nea
r re
gres
sion
on
th
e da
ta p
rovi
des
an r
val
ue
of 0
.03,
wh
ich
in
dica
tes
a po
or f
it. T
he
data
app
ears
to
be a
goo
d ca
ndi
date
for
a q
uad
rati
c re
gres
sion
.
Ste
p 1
E
nte
r th
e da
ta b
y pr
essi
ng
ST
AT
an
d se
lect
ing
the
Edi
t op
tion
. En
ter
the
year
s si
nce
197
0 as
you
r x-
valu
es (
L1)
an
d en
ter
the
popu
lati
on f
igu
res
as y
our
y-va
lues
(L
2).
Ste
p 2
P
erfo
rm t
he
quad
rati
c re
gres
sion
by
pres
sin
g S
TA
T a
nd
sele
ctin
g th
e C
AL
C o
ptio
n. S
crol
l do
wn
to
Qu
adR
eg a
nd
pres
s E
NT
ER
.
Ste
p 3
W
rite
th
e eq
uat
ion
of
the
best
-fit
par
abol
a by
rou
ndi
ng
the
a, b
, an
d c
valu
es o
n t
he
scre
en.
Th
e eq
uat
ion
for
th
e be
st-f
it p
arab
ola
is
y=
302
.8x2
– 1
1,48
0x +
501
,227
.b
. F
ind
th
e co
effi
cien
t of
det
erm
inat
ion
.
Th
e co
effi
cien
t of
det
erm
inat
ion
for
th
e pa
rabo
la i
s R
2 =
0.9
69,
wh
ich
in
dica
tes
a go
od f
it.
c. U
se t
he
qu
adra
tic-
regr
essi
on p
arab
ola
to p
red
ict
the
pop
ula
tion
in
201
0.
Gra
ph t
he
best
-fit
par
abol
a. T
hen
use
th
e T
RA
CE
fea
ture
an
d th
e ar
row
key
s u
nti
l yo
u f
ind
a po
int
wh
ere
x =
40.
Whe
n x
≈ 40
, y ≈
52
5,00
0. T
he e
stim
ated
pop
ulat
ion
wil
l be
525,
000.
Exer
cise
s
1. T
he
tabl
e be
low
sh
ows
the
aver
age
hig
h t
empe
ratu
re i
n C
ryst
al
Riv
er, F
lori
da i
n v
ario
us
mon
ths.
Mo
nth
Ja
n (
1)
Ma
r (3
)M
ay (
5)
Jul (7
)S
ep
(9
)N
ov (
11)
Avg
. Hig
h (
°F)
68
°76
°8
7°
91
°8
8°
76
°
Sour
ce: C
ount
ry S
tudi
es
a. F
ind
the
equ
atio
n o
f th
e be
st-f
it p
arab
ola.
y =
-0.
696x
2 +
9.5
x +
57.
20
b.
Fin
d th
e co
effi
cien
t of
det
erm
inat
ion
. R
2 =
0.
943
c. U
se t
he
quad
rati
c-re
gres
sion
par
abol
a to
pre
dict
th
e av
erag
e h
igh
tem
pera
ture
in
A
pril
(4t
h m
onth
).
Enri
chm
ent
Qu
ad
rati
c R
eg
ressio
n P
ara
bo
las
Exam
ple
abo
ut
84°F
4-6
036_
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10
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7 A
M
Answers (Lesson 4-6 and Lesson 4-7)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 4-7
Cha
pte
r 4
43
Gle
ncoe
Alg
ebra
1
Inve
rse
Rel
atio
ns
An
in
vers
e re
lati
on i
s th
e se
t of
ord
ered
pai
rs o
btai
ned
by
exch
angi
ng
the
x-co
ordi
nat
es w
ith
th
e y-
coor
din
ates
of
each
ord
ered
pai
r. T
he
dom
ain
of
a re
lati
on b
ecom
es t
he
ran
ge o
f it
s in
vers
e, a
nd
the
ran
ge o
f th
e re
lati
on b
ecom
es t
he
dom
ain
of
its
in
vers
e.
F
ind
an
d g
rap
h t
he
inve
rse
of t
he
rela
tion
rep
rese
nte
d b
y li
ne
a.
Th
e gr
aph
of
the
rela
tion
pas
ses
thro
ugh
(–2,
–10
), (–
1, –
7), (
0, –
4), (
1, –
1), (
2, 2
), (3
, 5),
and
(4, 8
).
To
fin
d th
e in
vers
e, e
xch
ange
th
e co
ordi
nat
es
of t
he
orde
red
pair
s.
Th
e gr
aph
of
the
inve
rse
pass
es t
hro
ugh
th
e po
ints
(–
10, –
2), (
–7,
–1)
, (–4,
0),
(–1,
1),
(2, 2
), (5
, 3),
and
(8, 4
). G
raph
th
ese
poin
ts a
nd
then
dra
w t
he
lin
e th
at p
asse
s th
rou
gh t
hem
.
Exer
cise
sF
ind
th
e in
vers
e of
eac
h r
elat
ion
.
1. {
(4, 7
), (6
, 2),
(9, –
1), (
11, 3
)}
2. {
(–5,
–9)
, (–4,
–6)
, (–2,
–4)
, (0,
–3)
}
3.
xy
–8
–15
–2
–11
1–
8
51
118
4.
x
y
–8
3
–2
9
213
618
819
5.
x
y
–6
14
–5
11
–4
8
–3
5
–2
2
Gra
ph
th
e in
vers
e of
eac
h r
elat
ion
.
6.
y
xO8 4
−4
−8
48
−4
−8
7.
y
xO8 4
−4
−8
48
−4
−8
8.
y
xO8 4
−4
−8
48
−4
−8
Stud
y G
uide
Invers
e L
inear
Fu
ncti
on
s
Exam
ple
{(7,
4),
(2, 6
), (-
1, 9
), (3
, 11)
}
{(-
15, -
8), (
-11
, -2)
, ( -
8, 1
), (1
, 5),
(8, 1
1)}
{(3,
-8)
, (9,
-2)
, (1
3, 2
), (1
8, 6
), (1
9, 8
)}{(
14, -
6), (
11, -
5),
(8, -
4), (
5, -
3), (
2, -
2)}
{(-
9, -
5), (
-6,
-4)
, (-
4, -
2), (
-3,
0)}
y
xO8 4
−4
−8
48
−4
−8
( −10
, −2)
( −4,
0)
( 2, 2
)( 8, 4
)
a
4-7
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Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 4 A21 Glencoe Algebra 1
Answers (Lesson 4-7)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 4
44
Gle
ncoe
Alg
ebra
1
Stud
y G
uide
(co
nti
nu
ed)
Invers
e L
inear
Fu
ncti
on
s
Inve
rse
Fun
ctio
ns
A l
inea
r re
lati
on t
hat
is
desc
ribe
d by
a f
un
ctio
n h
as a
n i
nve
rse
fun
ctio
n t
hat
can
gen
erat
e or
dere
d pa
irs
of t
he
inve
rse
rela
tion
. Th
e in
vers
e of
th
e li
nea
r fu
nct
ion
f (x
) ca
n b
e w
ritt
en a
s f -
1 (x)
an
d is
rea
d f
of x
in
vers
e or
th
e in
vers
e of
f o
f x.
F
ind
th
e in
vers
e of
f (x
) =
3 −
4 x +
6.
Ste
p 1
f (x
) =
3 −
4 x +
6
Ori
gin
al equation
y
= 3 −
4 x +
6
Repla
ce f
(x)
with y
.
Ste
p 2
x =
3 −
4 y +
6
Inte
rchange y
and x
.
Ste
p 3
x
- 6
= 3 −
4 y
Subtr
act
6 f
rom
each s
ide.
4 −
3 (x -
6)
= y
M
ultip
ly e
ach s
ide b
y 4
−
3 .
Ste
p 4
4 −
3 (x -
6) =
f -
1 (x)
R
epla
ce y
with f
-1 (x
).
Th
e in
vers
e of
f (x
) =
3 −
4 x +
6 i
s f -
1 (x)
= 4 −
3 (x -
6)
or f
-1 (
x) =
4 −
3 x -
8.
Exer
cise
sF
ind
th
e in
vers
e of
eac
h f
un
ctio
n.
1.
f (x)
= 4
x -
3
2.
f (x)
= -
3x +
7
3.
f (x)
= 3 −
2 x -
8
f
-1 (
x)
= x
+ 3
−
4
f -
1 (x)
= 7
- x
−
3
f -
1 (x)
= 2 −
3 x +
16
−
3
4.
f (x)
= 1
6 -
1 −
3 x
5.
f (x)
= 3
(x -
5)
6.
f (x)
= -
15 -
2 −
5 x
f
-1 (
x)
= -
3x +
48
f -
1 (x)
= x
−
3 + 5
f
-1 (
x)
= -
5 −
2 (x +
15)
7. T
OO
LS J
imm
y re
nts
a c
hai
nsa
w f
rom
th
e de
part
men
t st
ore
to w
ork
on h
is y
ard.
T
he
tota
l co
st C
(x)
in d
olla
rs i
s gi
ven
by
C(x
) =
9.9
9 +
3.0
0x, w
her
e x
is t
he
nu
mbe
r of
day
s h
e re
nts
th
e ch
ain
saw
.
a.
Fin
d th
e in
vers
e fu
nct
ion
C -
1 (x)
. C
-1 (x
) =
x -
9.9
9 −
3
b
. W
hat
do
x an
d C
-1 (
x) r
epre
sen
t in
th
e co
nte
xt o
f th
e in
vers
e fu
nct
ion
?
x re
pre
sen
ts t
he
tota
l co
st a
nd
C -
1 (x)
rep
rese
nts
th
e n
um
ber
o
f d
ays
he
ren
ts t
he
chai
nsa
w.
c.
How
man
y da
ys d
id J
imm
y re
nt
the
chai
nsa
w i
f th
e to
tal
cost
w
as $
27.9
9? 6
day
s
Exam
ple
4-7
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 4-7
Cha
pte
r 4
45
Gle
ncoe
Alg
ebra
1
Fin
d t
he
inve
rse
of e
ach
rel
atio
n.
1.
xy
–9
–1
–7
–4
–5
–7
–3
–10
–1
–13
2.
x
y
18
26
34
42
50
3.
x
y
–4
–2
–2
–1
01
20
42
4. {
(-3,
2),
(-1,
8),
(1, 1
4), (
3, 2
0)}
5. {
(5, -
3), (
2, -
9), (
-1,
-15
), (-
4, -
21)}
{
(2, -
3), (
8, -
1), (
14, 1
), (2
0, 3
)}
{(
-3,
5),
(-9,
2),
(-15
, -1)
, (-
21, -
4)}
6. {
(4, 6
), (3
, 1),
(2, -
4), (
1, -
9)}
7. {
(-1,
16)
, (-
2, 1
2), (
-3,
8),
(-4,
4)}
{
(6, 4
), (1
, 3),
(-4,
2),
(-9,
1)}
{(16
, -1)
, (12
, -2)
, (8,
-3)
, (4,
-4)
}
Gra
ph
th
e in
vers
e of
eac
h f
un
ctio
n.
8.
y
xO8 4
−4
−8
48
−4
−8
9.
y
xO8 4
−4
−8
48
−4
−8
10
. y
xO8 4
−4
−8
48
−4
−8
Fin
d t
he
inve
rse
of e
ach
fu
nct
ion
.
11.
f (x
) =
8x
- 5
12
. f (
x) =
6(x
+ 7
) 13
. f (
x) =
3 −
4 x +
9
f -
1 (x)
= x
+ 5
−
8
f -1 (
x)
= x
−
6 - 7
f -
1 (x)
= 4 −
3 (x -
9)
14.
f (x
) =
-16
+ 2 −
5 x
15.
f (x)
= 3x
+ 5
−
4
16.
f (x)
= -
4x +
1
−
5
f -
1 (x)
= 5 −
2 (x +
16)
f -
1 (x)
= 4x
- 5
−
3
f -1 (
x)
= 1
- 5x
−
4
17. L
EMO
NA
DE
Ch
riss
y sp
ent
$5.0
0 on
su
ppli
es a
nd
lem
onad
e po
wde
r fo
r h
er l
emon
ade
stan
d. S
he
char
ges
$0.5
0 pe
r gl
ass.
a.
Wri
te a
fu
nct
ion
P(x
) to
rep
rese
nt
her
pro
fit
per
glas
s so
ld.
P(x
) =
0.5
0x -
5.0
0
b
. F
ind
the
inve
rse
fun
ctio
n, P
-1 (
x).
P -
1 (x)
= x
+ 5
.00
−
0.50
c.
Wh
at d
o x
and
P -
1 (x)
rep
rese
nt
in t
he
con
text
of
the
inve
rse
fun
ctio
n?
x r
epre
sen
ts
the
tota
l pro
fi t a
nd
P -
1 (x)
rep
rese
nts
th
e n
um
ber
of
gla
sses
so
ld.
d
. How
man
y gl
asse
s m
ust
Ch
riss
y se
ll i
n o
rder
to
mak
e a
$3 p
rofi
t? 1
6
Skill
s Pr
acti
ceIn
vers
e L
inear
Fu
ncti
on
s
{(-
1, -
9), (
-4,
-7)
, (-
7, -
5),
(-10
, -3)
, (-
13, -
1)}
{(8,
1),
(6, 2
), (4
, 3),
(2, 4
), (0
, 5)}
{(-
2, -
4), (
-1,
-2)
, (1
, 0),
(0, 2
), (2
, 4)}
4-7
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Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF 2nd
Chapter 4 A22 Glencoe Algebra 1
Answers (Lesson 4-7)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 4-7
Cha
pte
r 4
47
Gle
ncoe
Alg
ebra
1
Wor
d Pr
oble
m P
ract
ice
Invers
e L
inear
Fu
ncti
on
s
1. B
USI
NES
S A
lish
a st
arte
d a
baki
ng
busi
nes
s. S
he
spen
t $3
6 in
itia
lly
on
supp
lies
an
d ca
n m
ake
5 do
zen
bro
wn
ies
at a
cos
t of
$12
. Sh
e ch
arge
s h
er
cust
omer
s $1
0 pe
r do
zen
bro
wn
ies.
a.
Wri
te a
fu
nct
ion
C(x
) to
rep
rese
nt
Ali
sha’
s to
tal
cost
per
doz
en
brow
nie
s. C
(x)
=36
+ 2
.4x
b.
Wri
te a
fu
nct
ion
E(x
) to
rep
rese
nt
Ali
sha’
s ea
rnin
gs p
er d
ozen
bro
wn
ies
sold
. E
(x)
=10
x
c.
Fin
d P
(x)
=E
(x)
-C
(x).
Wh
at d
oes
P (x
) re
pres
ent?
P(x
) =
7.6
x-
36;
P
(x)
rep
rese
nts
th
e p
rofi t
th
at
Alis
ha
earn
s.
d. F
ind
C -
1 (x)
, E -
1 (x)
, an
d P
-1 (
x).
C -
1 (x)
=
x -
36
−
2.4
; E
-1 (
x)
=x
− 10;
P -
1 (x)
=
x +
36
−
7.6
e.
How
man
y do
zen
bro
wn
ies
does
A
lish
a n
eed
to s
ell
in o
rder
to
mak
e a
prof
it?
5 o
r m
ore
2. G
EOM
ETRY
Th
e ar
ea o
f th
e ba
se o
f a
cyli
ndr
ical
wat
er t
ank
is 6
6 sq
uar
e fe
et.
Th
e vo
lum
e of
wat
er i
n t
he
tan
k is
de
pen
den
t on
th
e h
eigh
t of
th
e w
ater
han
d is
rep
rese
nte
d by
th
e fu
nct
ion
V
(h)
= 6
6h. F
ind
V -
1 (h
). W
hat
wil
l th
e h
eigh
t of
th
e w
ater
be
wh
en t
he
volu
me
reac
hes
231
0 cu
bic
feet
?
V -
1 (h
) =
h− 66
; 35
fee
t
3. S
ERV
ICE
A t
ech
nic
ian
is
wor
kin
g on
a
furn
ace.
He
is p
aid
$150
per
vis
it p
lus
$70
for
ever
y h
our
he
wor
ks o
n t
he
furn
ace.
a.
Wri
te a
fu
nct
ion
C(x
) to
rep
rese
nt
the
tota
l ch
arge
for
eve
ry h
our
of
wor
k. C
(x)
= 7
0x+
150
b
. F
ind
the
inve
rse
fun
ctio
n, C
-1 (
x).
C -
1 (x)
=
x -
150
−
70
c. H
ow l
ong
did
the
tech
nic
ian
wor
k on
th
e fu
rnac
e if
th
e to
tal
char
ge w
as
$640
? 7
ho
urs
4. F
LOO
RIN
G K
ara
is h
avin
g ba
sebo
ard
inst
alle
d in
her
bas
emen
t. T
he
tota
l co
st C
(x)
in d
olla
rs i
s gi
ven
by
C(x
) =
125
+ 1
6x, w
her
e x
is t
he
nu
mbe
r of
pie
ces
of w
ood
requ
ired
fo
r th
e in
stal
lati
on.
a.
Fin
d th
e in
vers
e fu
nct
ion
C -
1 (x)
.
C -
1 (x)
=
x -
125
−
16
b.
If t
he
tota
l co
st w
as $
269
and
each
pi
ece
of w
ood
was
12
feet
lon
g, h
ow
man
y to
tal
feet
of
woo
d w
ere
use
d? 1
08 f
eet
5. B
OW
LIN
G L
ibby
’s f
amil
y w
ent
bow
lin
g du
rin
g a
hol
iday
spe
cial
. Th
e sp
ecia
l co
st
$40
for
pizz
a, b
owli
ng
shoe
s, a
nd
un
lim
ited
dri
nks
. Eac
h g
ame
cost
$2.
H
ow m
any
gam
es d
id L
ibby
bow
l if
th
e to
tal
cost
was
$11
2 an
d th
e si
x fa
mil
y m
embe
rs b
owle
d an
equ
al n
um
ber
of
gam
es?
6
4-7
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 4
46
Gle
ncoe
Alg
ebra
1
Fin
d t
he
inve
rse
of e
ach
rel
atio
n.
1. {
(-2,
1),
(-5,
0),
(-8,
-1)
, (-
11, 2
)}
2. {
(3, 5
), (4
, 8),
(5, 1
1), (
6, 1
4)}
{
(1, -
2), (
0, -
5), (
-1,
-8)
, (2,
-11
)}
{(5,
3),
(8, 4
), (1
1, 5
), (1
4, 6
)}
3. {
(5, 1
1), (
1, 6
), (-
3, 1
), (-
7, -
4)}
4. {
(0, 3
), (2
, 3),
(4, 3
), (6
, 3)}
{
(11,
5),
(6, 1
), (1
, -3)
, (-
4, -
7)}
{(3,
0),
(3, 2
), (3
, 4),
(3, 6
)}
Gra
ph
th
e in
vers
e of
eac
h f
un
ctio
n.
5.
y
xO8 4
−4
−8
48
−4
−8
6.
y
xO8 4
−4
−8
48
−4
−8
7.
y
xO8 4
−4
−8
48
−4
−8
Fin
d t
he
inve
rse
of e
ach
fu
nct
ion
.
8.
f (x)
= 6 −
5 x -
3
9.
f (x)
= 4x
+ 2
−
3
10.
f (x)
= 3x
- 1
−
6
f -
1 (x)
= 5 −
6 (x +
3)
f -1 (
x)
= 3x
- 2
−
4
f -1 (
x)
= 6x
+ 1
−
3
11.
f (x
) =
3(3
x +
4)
12.
f (x)
= -
5(-
x -
6)
13.
f (x)
= 2x
- 3
−
7
f -
1 (x)
= x
−
3 - 4
−
3
f -1 (
x)
= x
−
5 - 6
f -
1 (x)
= 7x
+ 3
−
4
Wri
te t
he
inve
rse
of e
ach
eq
uat
ion
in
f -
1 (x)
not
atio
n.
13.
4x
+ 6
y =
24
14.
-3y
+ 5
x =
18
15.
x +
5y
= 1
2
f -
1 (x)
= 24
- 6x
−
4
f -1 (
x)
= 3x
+ 1
8 −
5
f -1 (
x)
= -
5x +
12
16.
5x
+ 8
y =
40
17.
-4y
- 3
x =
15
+ 2
y 18
. 2x
- 3
= 4
x +
5y
f -
1 (x)
= 40
- 8x
−
5
f -1 (
x)
= -
2x -
5
f -1 (
x)
= -
5x -
3
−
2
19. C
HA
RIT
Y J
enn
y is
ru
nn
ing
in a
ch
arit
y ev
ent.
On
e do
nor
is
payi
ng
an i
nit
ial
amou
nt
of
$20.
00 p
lus
an e
xtra
$5.
00 f
or e
very
mil
e th
at J
enn
y ru
ns.
a.
Wri
te a
fu
nct
ion
D(x
) fo
r th
e to
tal
don
atio
n f
or x
mil
es r
un
. D
(x)
= 5
x +
20
b
. F
ind
the
inve
rse
fun
ctio
n, D
-1 (
x).
D -
1 (x)
= x
- 2
0 −
5
c.
Wh
at d
o x
and
D -
1 (x)
rep
rese
nt
in t
he
con
text
of
the
inve
rse
fun
ctio
n?
x r
epre
sen
ts
the
tota
l do
nat
ion
an
d P
-1 (x
) re
pre
sen
ts t
he
nu
mb
er m
iles
run
.
Prac
tice
Invers
e L
inear
Fu
ncti
on
s
4-7
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An
swer
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Chapter 4 A23 Glencoe Algebra 1
Answers (Lesson 4-7)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 4
48
Gle
ncoe
Alg
ebra
1
In a
fu
nct
ion
, th
ere
is e
xact
ly o
ne
outp
ut
for
ever
y in
put.
In
oth
er w
ords
, eve
ry e
lem
ent
in
the
dom
ain
pai
rs w
ith
exa
ctly
on
e el
emen
t in
th
e ra
nge
. Wh
en a
fu
nct
ion
is
one-
to-o
ne,
ea
ch e
lem
ent
of t
he
dom
ain
pai
rs w
ith
exa
ctly
on
e u
niq
ue
elem
ent
in t
he
ran
ge. W
hen
a
fun
ctio
n i
s on
to, e
ach
ele
men
t of
th
e ra
nge
cor
resp
onds
to
an e
lem
ent
in t
he
dom
ain
.
If a
fu
nct
ion
is
both
on
e-to
-on
e an
d on
to, t
hen
th
e in
vers
e is
als
o a
fun
ctio
n.
Det
erm
ine
wh
eth
er e
ach
rel
atio
n i
s a
fun
ctio
n. I
f it
is
a fu
nct
ion
, det
erm
ine
if i
t is
on
e-to
-on
e, o
nto
, bot
h, o
r n
eith
er.
1.
11 16-
3 4
3 6 9 12
2.
1 2 3 4 5
-3
-2 0 4 5
3.
3 6 9 12 15
10 5 0-
5
4.
4 2 7 11 6
1-
2-
4 7
5.
2 6 13
2 3 4 6 8
6.
3 1
-9 10
2 4 11 17 19
Det
erm
ine
wh
eth
er t
he
inve
rse
of e
ach
fu
nct
ion
is
also
a f
un
ctio
n.
7.
y
xO8 4
−4
−8
48
−4
−8
8.
y
xO8 4
−4
−8
48
−4
−8
9.
y
xO8 4
−4
−8
48
−4
−8
Enri
chm
ent
On
e-t
o-O
ne a
nd
On
to F
un
cti
on
s
nei
ther
on
to
no
bo
th
nei
ther
no
on
to
on
e-to
-on
e
yes
2 6 9 12
-1 3 5 8 9
one–
to–o
ne
-3
-2
-1 2 6
3 5 10
onto
5 7 9 10
-6
-11
-15
-19
both
4-7
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Chapter 4 A25 Glencoe Algebra 1
Chapter 4 Assessment Answer KeyQuiz 1 (Lessons 4-1 and 4-2) Quiz 3 (Lessons 4-5 and 4-6) Mid-Chapter TestPage 51 Page 52 Page 53
Quiz 2 (Lessons 4-3 and 4-4)
Page 51Quiz 4 (Lesson 4-7)
Page 52
1.
2.
3.
4.
5.
positive correlation; the older a person is, the higher the median income
y = 4.09x - 90.74
D
about $36,000
Age (years)
Med
ian
Inco
me
($10
00)
16
19
22
25
28
31
260 27 28 29 30
f -1 (x) = x - 6
−
4
1.
2.
3.
4.
5.
{(3, 1), (-1, 4),
(-5, 7), (-9, 10)}
f -1 (x) = 4 −
3 (x + 8)
A
y
xO
8
4
−4−8 4 8
−4
−8
1. A
2. H
3. B
4. J
5. D
6. H
7. t = 20h + 50
8.
9. $130
10. 6.5 hours
1
Hours2 3 4 5 6 7 8 9 10
20406080
100
Tota
l Cos
t ($)
120140160180200
1.
2.
3. y
xO
4.
5.
y =
1 −
4 x - 5
y = -
4 −
11 x +
58 −
11
h = 3y + 48 for h in
inches or h = 0.25y + 4
for h in feet
C
1.
2.
3.
4.
5.
y - 6 = - 1 −
3 (x - 3)
y = -x + 7
y + 1 = 0
y = -
1 −
3 x + 14
−
3
D
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Chapter 4 A26 Glencoe Algebra 1
Chapter 4 Assessment Answer KeyVocabulary Test Form 1Page 54 Page 55 Page 56
1. perpendicular lines
2. inverse relation
3. scatter plot
4. parallel lines
5. correlation coefficient
6. linear interpolation
7.
linear extrapolation
8. slope-intercept
9. point-slope
10.
Sample answer: A line of fi t
is a line that comes close to the data points for a scatter plot, even if all the data
points do not lie on that line.
11.
Sample answer: Linear
extrapolation is the process of using a linear equation to
predict a y-value for an x-value that lies beyond the extremes of the domain of
the relation.
1. C
2. H
3. D
4. F
5. A
6. H
7. C
8. H
9. B
10. G
11. BB: 7
12.
13.
14.
15.
16.
17.
18.
19.
20.
F
B
F
D
J
C
H
C
G
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An
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s
PDF Pass
Chapter 4 A27 Glencoe Algebra 1
Chapter 4 Assessment Answer KeyForm 2A Form 2BPage 57 Page 58 Page 59 Page 60
1. D
2. H
3. D
4. H
5. B
6. G
7. D
8. H
9. B
10. F
11. D
12. F
13. B
14. G
15. C
16. G
17. C
18. H
19. B
20. J
1. B
2. F
3. C
4. G
5. A
6. F
7. D
8. H
9. B
10. G
11. B
12. F
13. B
14. F
15. C
16. J
17. D
18. J
19. B
20. H
B: -21
B: 17
−
3
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Chapter 4 A28 Glencoe Algebra 1
Chapter 4 Assessment Answer KeyForm 2CPage 61 Page 62
1. y = 0.10x + 28.75
2. 5x + 7y = 14
3. y =
2 −
3 x - 2
4. y
xO
5. y =
3 −
2 x -
1 −
2
6. x = -6
7. y - 8 =
1 −
3 (x + 2)
8. 12x + 7y = -16
9. y = 3x - 10
10. y = -2x + 1
11. y =
2 −
3 x - 4
12. y = 1.25x + 2508
13.
14.
Sample answer: using
data points (20, 67) and
(40, 87), y = x + 47; 82
15.
No, because the maximum score is 100%, even for very large amounts of time studying.
16. y = 0.52x - 983.73
17. 30
18. y
xO
8
4
−4−8 4 8
−4
−8
19. f -1 (x) =
5 - 15x −
4
20. f -1 (x) =
13 - 8x −
6
B: � = 1.2t + 1.8; 6 years
Time Spent Studying(minutes)
Sco
re R
ecei
ved
(per
cen
t)
0
60
70
80
90
100
10 20 30 40 50
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Chapter 4 A29 Glencoe Algebra 1
Chapter 4 Assessment Answer KeyForm 2DPage 63 Page 64
1. y = 2.50x + 4.95
2. x - y = 2
3. y = -
2 −
3 x - 2
4. y
xO
5. y = -5x + 29
6. x = 5
7. y =
4 −
3 (x - 3)
8. 2x + 3y = -1
9. y =
3 −
4 x -
5 −
4
10. y = -3x + 18
11. y = -
1 −
4 x + 4
12.
13.
14.
Sample answer:
using data points (30, 6.1) and
(70, 4.7), y = -0.035x + 7.15; about 4.9
15.
No, younger people are
likely to spend a
signifi cant percentage on
entertainment because of
a lack of other expenses.
16. y = 0.25x - 467.83
17. 35
18. y
xO
8
4
−4−8 4 8
−4
−8
19. f -1 (x) =
8 - 18x −
3
20. f -1 (x) =
28 + 3x −
5
B: y =
6 −
5 x - 6
Age
Perc
ent
Spen
t o
nEn
tert
ain
men
t
3
4
5
6
300 40 50 60 70 80
y = 8.35x -
16,766.5
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Chapter 4 A30 Glencoe Algebra 1
Chapter 4 Assessment Answer KeyForm 3Page 65 Page 66
1. y = 3x - 8
2. y =
5 −
2 x - 11
3. y = -
3 −
5 x +
26 −
5
4. y = 6
5. y - 1= -
3 −
5 (x - 2)
6. 2x + y = 1
7.
8. 2x + 3y = 6
9. y + 2 = -
2 −
3 x
10. x = 3
11. y = -
4 −
3 x - 9
12. y =
3 −
5 x - 6
13. y = 5
y
xO
14.
15.
positive; a verbal score is closely associated with the math score
16.
Sample answer: Using
data points (424, 466) and
(460, 488); y = 0.6x + 211.6;
about 479
17.
y = -2.67x + 45.17;
about 24 seats
18. y
xO
8
4
−4−8 4 8
−4
−8
19. f -1 (x) =
12 - 8x −
15
20. f -1 (x) =
13 + 3x −
2
B: 9
Verbal Score
Mat
h S
core
450
460
470
480
490
500
4000 440 480
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Chapter 4 A31 Glencoe Algebra 1
Chapter 4 Assessment Answer KeyPage 67, Extended-Response Test
Scoring Rubric
Score General Description Specifi c Criteria
4 Superior
A correct solution that
is supported by well-
developed, accurate
explanations
• Shows thorough understanding of the concepts of slope, various forms of a linear equation, graphing lines from an equation, scatter plots, correlation, and predicting data.
• Uses appropriate strategies to solve problems.
• Computations are correct.
• Written explanations are exemplary.
• Graphs are accurate and appropriate.
• Goes beyond requirements of some or all problems.
3 Satisfactory
A generally correct solution,
but may contain minor fl aws
in reasoning or computation
• Shows an understanding of the concepts of slope, various forms of a linear equation, graphing lines from an equation, scatter plots, correlation, and predicting data.
• Uses appropriate strategies to solve problems.
• Computations are mostly correct.
• Written explanations are effective.
• Graphs are mostly accurate and appropriate.
• Satisfi es all requirements of problems.
2 Nearly Satisfactory
A partially correct
interpretation and/or
solution to the problem
• Shows an understanding of most of the concepts of slope, various forms of a linear equation, graphing lines from an equation, scatter plots, correlation, and predicting data.
• May not use appropriate strategies to solve problems.
• Computations are mostly correct.
• Written explanations are satisfactory.
• Graphs are mostly accurate.
• Satisfi es the requirements of most of the problems.
1 Nearly Unsatisfactory
A correct solution with no
supporting evidence or
explanation
• Final computation is correct.
• No written explanations or work is shown to substantiate
the fi nal computation.
• Graphs may be accurate but lack detail or explanation.
• Satisfi es minimal requirements of some of the problems.
0 Unsatisfactory
An incorrect solution
indicating no mathematical
understanding of the
concept or task, or no
solution is given
• Shows little or no understanding of most of the concepts of
slope, various forms of a linear equation, graphing lines from an equation, scatter plots, correlation, and predicting data.
• Does not use appropriate strategies to solve problems.
• Computations are incorrect.
• Written explanations are unsatisfactory.
• Graphs are inaccurate or inappropriate.
• Does not satisfy requirements of problems.
• No answer may be given.
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Chapter 4 A32 Glencoe Algebra 1
1a. In order to graph the line through (-2, 3) you need to know the slope of the line, another point on the line, or the equation of the line.
1b. If you knew the slope of the line, you could plot another point using the rise and run on a coordinate plane. If you knew another point, you could graph that point and draw a line through (-2, 3) and the other point. If you knew the equation of the line, you could use the slope-intercept form of the equation to find the slope and intercept for graphing or you could use the equation and substitution to find another point on the line.
2a. The points have a strong negative correlation. This means that as x increases, y decreases.
2b. One example is the longer a candle burns, the shorter it gets. Another is the longer you run a car, the less gasoline is left in the tank.
2c. See students’ work.
3a.
50
55
60
65
70
75
80
'20'30'40'50'60'70'80 '90 '00Year of Birth
Life
Exp
ecta
ncy
(yea
rs)
3b. While students’ knowledge from other experiences may lead them to that conclusion, there may be other factors that contribute to increased longevity. The information on the graph only leads us to claim that life expectancy is increasing.
3c. A regression equation calculated by a graphing calculator would yield a prediction of 78.9 years. However, students may look at the era since 1980 and notice that each 5-year period is about 0.3 year less than the previous 5-year period increase. This pattern would yield a prediction of about 75.9 years.
In addition to the scoring rubric found on page A31, the following sample answers may be used as guidance in evaluating extended-response assessment items.
Chapter 4 Assessment Answer Key Page 67, Extended-Response Test
Sample Answers
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Chapter 4 A33 Glencoe Algebra 1
1. A B C D
2. F G H J
3. A B C D
4. F G H J
5. A B C D
6. F G H J
7. A B C D
8. F G H J
9. A B C D
10. F G H J
Chapter 4 Assessment Answer KeyStandardized Test PracticePage 68 Page 69
11. A B C D
12. F G H J
13. A B C D
14. F G H J
15. 16.
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
. . . . .
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
21 9
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
. . . . .
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
.8
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Chapter 4 A34 Glencoe Algebra 1
Chapter 4 Assessment Answer KeyStandardized Test PracticePage 70
17. 2r2t2
18. 0
19. -18
20. 21
21. 32
22. 16
23. -30 y
24. -2a + 3b
25. -8
26. 8 −
9
27. -7
28.
{-7.5, -6.5, -6,
-5, -3.5}
29.
Yes; exactly one member of the range is paired with each member of the
domain.
30. y =
3 −
2 x + 2
31. 5 −
7
32. y = -3x + 12
33. x = -6
34a. $2 per year
34b. $21.50
A25_A36_ALG1_A_CRM_C04_AN_660499.indd A34A25_A36_ALG1_A_CRM_C04_AN_660499.indd A34 12/21/10 1:24 AM12/21/10 1:24 AM