Name ________________________________________ Date __________________ Class__________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
5-3 Holt McDougal Algebra 1
Practice A Identifying Linear Functions
Use the graph for 1–3. 1. Is this graph a function? _______________
2. Explain how you know it is a function.
____________________________________________________
____________________________________________________
3. If this graph is a function, is it also a linear function? _______________
Use the set {(1, 8), (2, 6), (3, 4), (4, 2), (5, 0)} for 4–5.
4. Does the set of ordered pairs satisfy a linear function? ___________________________ 5. Explain how you decided. __________________________________________________________
_________________________________________________________________________________________
6. Write the equation y = x − 4 in standard form (Ax + By = C).
_________________________________________
7. Is y = x − 4 a linear function?
_________________________________________
8. Graph y = x − 4 to check. 9. In 2005, a storm in Milwaukee, WI was dropping 2.5
inches of snow every hour. The total amount of snow is given by f(x) = 2.5x, where x is the number of hours. Graph this function and give its domain and range.
_________________________________________
LESSON
5-1
Name ________________________________________ Date __________________ Class__________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
5-4 Holt McDougal Algebra 1
Practice B Identifying Linear Functions
Identify whether each graph represents a function. Explain. If the graph does represent a function, is the function linear?
1. ___________________________________________________________
___________________________________________________________
___________________________________________________________
2. ___________________________________________________________
___________________________________________________________
___________________________________________________________ 3. Which set of ordered pairs satisfies a linear function? Explain. Set A: {(5, 1), (4, 4), (3, 9), (2, 16), (1, 25)} _________________________________________
Set B: {(1, −5), (2, −3), (3, −1), (4, 1), (5, 3)} _________________________________________
4. Write y = −2x in standard form. Then graph the function.
______________________________________________________
5. In 2005, the Shabelle River in Somalia rose an estimated 5.25 inches every hour for 15 hours. The increase in water level is represented by the function f(x) = 5.25x, where x is the number of hours. Graph this function and give its domain and range.
______________________________________________________
LESSON
5-1
Name ________________________________________ Date __________________ Class__________________
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5-11 Holt McDougal Algebra 1
Practice A Using Intercepts
Find the x- and y-intercepts. 1.
2. 3.
x-intercept: _____________ x-intercept: _____________ x-intercept: _____________ y-intercept: _____________ y-intercept: _____________ y-intercept: _____________ 4. Find the intercepts of 2x + 3y = 6 by following the steps below.
a. Substitute y = 0 into the equation. Solve for x.
_______________________________________________
b. The x-intercept is: ________________________ c. Substitute x = 0 into the equation. Solve for y.
_______________________________________________
d. The y-intercept is: ________________________ e. Use the intercepts to graph the line described by the equation.
5. Jennifer started with $50 in her savings account. Each week she withdrew $10. The amount of money in her savings account after x weeks is represented by the function f(x) = 50 − 10x. a. Find the intercepts and graph the function.
_______________________________________________
b. What does each intercept represent?
_______________________________________________
_______________________________________________
_______________________________________________
LESSON
5-2
Name ________________________________________ Date __________________ Class__________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
5-12 Holt McDougal Algebra 1
Practice B Using Intercepts
Find the x- and y-intercepts. 1.
2.
3.
________________________ _________________________ ________________________
________________________ ________________________ ________________________
Use intercepts to graph the line described by each equation.
4. 3x + 2y = −6 5. x − 4y = 4
6. At a fair, hamburgers sell for $3.00 each and hot dogs sell for
$1.50 each. The equation 3x + 1.5y = 30 describes the number of hamburgers and hot dogs a family can buy with $30. a. Find the intercepts and graph the function.
_______________________________________________
b. What does each intercept represent?
_______________________________________________
_______________________________________________
_______________________________________________
_______________________________________________
LESSON
5-2
Name ________________________________________ Date __________________ Class__________________
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5-19 Holt McDougal Algebra 1
Practice A Rate of Change and Slope
Fill in the blanks to define slope. 1. The ___________ is the difference in the y-values of two points on a line. 2. The ___________ is the difference in the x-values of two points on a line. 3. The slope of a line is the ratio of ___________ to ___________ for any two points on the line.
Find the rise and run between each set of points. Then, write the slope of the line. 4.
5.
6.
slope = _______________ slope = _______________ slope = _______________
Tell whether the slope of each line is positive, negative, zero, or undefined. 7.
8.
9.
________________________ _________________________ ________________________
10. The table shows a truck driver’s distance from home during one day’s deliveries. Find the rate of change for each time interval.
Time (h) 0 1 4 5 8 10
Distance (mi) 0 35 71 82 199 200
Hour 0 to Hour 1: _________ Hour 1 to Hour 4: _________ Hour 4 to Hour 5: _________
Hour 5 to Hour 8: _________ Hour 8 to Hour 10: _________
The rate of change represents the average speed. During which time interval was the driver’s average speed the least? _________________________________
LESSON
5-3
Name ________________________________________ Date __________________ Class__________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
5-20 Holt McDougal Algebra 1
Practice B Rate of Change and Slope
Find the rise and run between each set of points. Then, write the slope of the line.
1.
2.
3.
rise = ______ run = ______ rise = ______ run = ______ rise = ______ run = ______
slope = _______________ slope = _______________ slope = _______________
4.
5.
6.
rise = ______ run = ______ rise = ______ run = ______ rise = ______ run = ______
slope = _______________ slope = _______________ slope = _______________
Tell whether the slope of each line is positive, negative, zero, or undefined. 7.
8.
9.
________________________ _________________________ ________________________
10. The table shows the amount of water in a pitcher at different times. Graph the data and show the rates of change. Between which two hours is the rate of change the greatest? _______________
Time (h) 0 1 2 3 4 5 6 7
Amount (oz) 60 50 25 80 65 65 65 50
LESSON
5-3
Name ________________________________________ Date __________________ Class__________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
5-27 Holt McDougal Algebra 1
Practice A The Slope Formula
Find the slope of the line that contains each pair of points. 1. (3, 1) and (9, 2) 2. (−2, 3) and (2, −1) 3. (4, 6) and (0, −2)
m = 2 1
2 1
y yx x
−−
m = 2 1
2 1
y yx x
−−
m = 2 1
2 1
y yx x
−−
= 2 1
−−
= 1
= 1 2 − −−
=
= =
−−
=
=
Each graph or table shows a linear relationship. Find the slope. 4. 5. 6.
________________________ _________________________ ________________________
Find the slope of each line. Then tell what the slope represents. 7. 8.
_________________________________________ ________________________________________
_________________________________________ ________________________________________
Complete the steps to find the slope of the line described by 2x + 5y = 10. 9. a. Find the x-intercept. b. Find the y-intercept. c. The line contains (____, 0) Let y = 0 Let x = 0 and (0, _____). Use the 2x + 5 (_____) = −10 2 (_____) + 5y = −10 slope formula.
_______ = −10 _______ = −10
÷ _______ ÷ _______ ÷ _______ ÷ _______
x = ________ y = ________
LESSON
5-4
x y
0 82
3 76
6 70
9 64
12 58
m = 2 1
2 1
y yx x
−−
= 00
−−
=
Name ________________________________________ Date __________________ Class__________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
5-28 Holt McDougal Algebra 1
Practice B The Slope Formula
Find the slope of the line that contains each pair of points. 1. (2, 8) and (1, −3) 2. (−4, 0) and (−6, −2) 3. (0, −2) and (4, −7)
m = 2 1
2 1
y yx x
−−
m = 2 1
2 1
y yx x
−−
m = 2 1
2 1
y yx x
−−
=
−−
=
−−
=
−−
=
= =
= =
Each graph or table shows a linear relationship. Find the slope. 4. 5. 6.
________________________ _________________________ ________________________
Find the slope of each line. Then tell what the slope represents. 7. 8.
_________________________________________ ________________________________________
_________________________________________ ________________________________________
Find the slope of the line described by each equation. 9. 3x + 4y = 24 10. 8x + 48 = 3y
_________________________________________ ________________________________________
LESSON
5-4
x y
1 3.75
2 5
3 6.25
4 7.50
5 8.75
Name ________________________________________ Date __________________ Class__________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
5-43 Holt McDougal Algebra 1
Practice A Direct Variation
Complete the table.
Solve for y (if needed).
Is the equation in the form y = kx?
Is it a direct variation?
Constant of variation
1. y = 7x y = 7x yes yes
2. y = 4x − 10
3. 5x − 2y = 0
Complete the table.
Find the value of yx
for each ordered pair.
Is the value of yx
the same
for each ordered pair?
Direct variation?
4.
5.
6. The value of y varies directly with x, and y = −2 when x = −4. Find y when x = 8.
Find k: Use k to find y: y = kx y = kx −2 = k(−4) y =
_____( ) _____( )
______ = k y = __________
7. The value of y varies directly with x, and y = 12 when x = 8. Find y when x = 15.
Find k: Use k to find y: y = kx y = kx 12 = k(8) y =
_____( ) _____( )
_____ = k y = __________ 8. The number of hamburgers that can be
made varies directly with the weight of ground beef used. Four hamburgers can be produced from every pound of ground beef. Write a direct variation equation for the number of hamburgers y that can be produced from x pounds of ground beef. Then graph the relationship.
_________________________________________
LESSON
5-5
x 4 8 12 y 16 20 24
x 10 15 20 y 2 3 4
Name ________________________________________ Date __________________ Class__________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
5-44 Holt McDougal Algebra 1
Practice B Direct Variation
Tell whether each equation is a direct variation. If so, identify the constant of variation. 1. y = 3x _________________ 2. y = 2x − 9 _________________ 3. 2x + 3y = 0 _________________ 4. 3y = 9x _________________
Find the value of yx for each ordered pair. Then, tell whether each
relationship is a direct variation.
5. x 6 15 21
y 2 5 7
yx
6. x 6 10 25
y 24 40 100
yx
7. x 10 15 20
y 3 5 9
yx
________________________ _________________________ ________________________
8. The value of y varies directly with x, and y = −18 when x = 6. Find y when x = −8.
Find k: Use k to find y:
y = kx
y = _____( ) _____( )
_____ = k y = __________
9. The value of y varies directly with x,
and y = 12
when x = 5.
Find y when x = 30.
Find k: Use k to find y:
y = kx
y = _____( ) _____( )
_____ = k y = __________ 10. The amount of interest earned in a savings account
varies directly with the amount of money in the account. A certain bank offers a 2% savings rate. Write a direct variation equation for the amount of interest y earned on a balance of x. Then graph.
_________________________________________
11. Another bank offers a different savings rate. If an account with $400 earns interest of $6, how much interest is earned by an account with $1800?
_________________________________________
LESSON
5-5
Name ________________________________________ Date __________________ Class__________________
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5-51 Holt McDougal Algebra 1
Practice A Slope-Intercept Form
Write the equation that describes each line in slope-intercept form.
1. slope = 23
; y-intercept = 2
y = ______ x + ______ 2. slope = −1; y-intercept = −8 y = ______ x − ______
3. slope = −2; (3, 5) is on the line. Find the y-intercept: y = mx + b
5 = (−2)(___) + b5 = ___+ b
+ ____+ ________ = b
Write the equation: y = ______ x + ______
Write each equation in slope-intercept form. Then graph the line.
4. y − 2x = −4 5. y − 3 = − 12
x 6. 2x + 3y = 6
________________________ _________________________ ________________________
7. A school orders 25 desks for each classroom,
plus 30 spare desks. The total number ordered as a function of the number of classrooms is shown in the graph. a. Write the equation represented by the graph.
_____________________________________
b. Identify the slope and y-intercept and describe their meanings. ________________________________________
____________________________________________________
c. Find the total number of desks ordered if there are 24 classrooms.
___________________________________________________
LESSON
5-6
Name ________________________________________ Date __________________ Class__________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
5-52 Holt McDougal Algebra 1
Practice B Slope-Intercept Form
Write the equation that describes each line in slope-intercept form. 1. slope = 4; y-intercept = −3 y = _______________________ 2. slope = −2; y-intercept = 0 y = _______________________
3. slope = − 1
3; y-intercept = 6
y = _______________________
4. slope = 25
, (10, 3) is on the line.
Find the y-intercept y = mx + b
____ = (____)____ + b
____ = ____ + b
____ = b
Write the equation: y = ______________
Write each equation in slope-intercept form. Then graph the line described by the equation.
5. y + x = 3 6. y + 4 = 43
x 7. 5x − 2y = 10
________________________ _________________________ ________________________
8. Daniel works as a volunteer in a homeless shelter.
So far, he has worked 22 hours, and he plans to continue working 3 hours per week. His hours worked as a function of time is shown in the graph.
a. Write an equation that represents the hours Daniel will work as a function of time. _____________________ b. Identify the slope and y-intercept and describe their meanings. ________________________________________
___________________________________________________
c. Find the number of hours worked after 16 weeks.
___________________________________________________
LESSON
5-6
Name ________________________________________ Date __________________ Class__________________
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5-59 Holt McDougal Algebra 1
Practice A Point-Slope Form
Match each graph with the correct slope and point.
1. slope = 12 ; (0, 2) ______ 2. slope = −
12 ; (2, 0) ______ 3. slope = −2; (2, 0) ______
A B C
Write an equation in point-slope form for the line with the given slope that contains the given point.
4. slope = 4; (3, 8) 5. slope = −12 ; (5, −3)
_________________________________________ ________________________________________
Write the equation that describes each line in slope-intercept form. 6. slope = 5; (1, 7) is on the line 7. slope = −3; (4, 0) is on the line
_________________________________________ ________________________________________
8. (0, 2) and (2, 6) are on the line 9. (8, −2) and (4, −4) are on the line
_________________________________________ ________________________________________
Find the intercepts of the line that contains each pair of points. 10. (2, 5) and (−6, 25) __________________ 11. (2, 9) and (−4, −9) __________________
12. The cost to have T-shirts made with the school logo is a function
of the number of T-shirts ordered. The costs for 20, 50, and 100 shirts are shown. Write an equation in slope-intercept form that represents the function. Then find the cost of ordering 130 T-shirts.
_________________________________________
LESSON
5-7
T-shirts 20 50 100Cost ($) 190 430 830
Name ________________________________________ Date __________________ Class__________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
5-60 Holt McDougal Algebra 1
Practice B Point-Slope Form
Write an equation in point-slope form for the line with the given slope that contains the given point. 1. slope = 3; (−4, 2) 2. slope = −1; (6, −1)
_________________________________________ ________________________________________
Graph the line described by each equation.
3. y + 2 = − 2
3 (x − 6) 4. y + 3 = − 2 (x − 4)
Write the equation that describes the line in slope-intercept form.
5. slope = −4; (1, −3) is on the line 6. slope = 12
; (−8, −5) is on the line
_________________________________________ ________________________________________
7. (2, 1) and (0, −7) are on the line 8. (−6, −6) and (2, −2) are on the line
_________________________________________ ________________________________________
Find the intercepts of the line that contains each pair of points. 9. (−1, −4) and (6, 10) __________________ 10. (3, 4) and (−6, 16) __________________
11. The cost of internet access at a cafe is a function of time. The costs for 8, 25, and 40 minutes are shown. Write an equation in slope-intercept form that represents the function. Then find the cost of surfing the web at the cafe for one hour.
_________________________________________
LESSON
5-7
Time (min) 8 25 40 Cost ($) 4.36 7.25 9.80
Name ________________________________________ Date __________________ Class__________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
5-67 Holt McDougal Algebra 1
Practice A Slopes of Parallel and Perpendicular Lines
Circle the equations whose lines are parallel.
1. y = 4; y = 12
x + 3; y = 12
x; y = 2x
2. y − 5 = 6(x + 2); y = −6x; 6x + y = 4; y = 6 3. Find the slope of each segment.
slope of AB : ____________________________
slope of AD : ____________________________
slope of DC : ____________________________
slope of BC : ____________________________ Explain why ABCD is a parallelogram.
_________________________________________________________________________________________
_________________________________________________________________________________________
Circle the equations whose lines are perpendicular. 4. y = x − 4; y = 3; y = −x; y = −3
5. y = 5x + 1; y = 3; y = 15
x; x = 5
6. y = 13
x − 2; x = 2; y − 4 = 3(x + 3); y = −3x + 9
7. Find the slope of each segment.
slope of AB : ______________________________
slope of BC : _____________________________
slope of AC : ____________________________
Explain why ABC is a right triangle.
_________________________________________________________________________________________
_________________________________________________________________________________________
LESSON
5-8
Name _______________________________________ Date __________________ Class__________________
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5-68 Holt McDougal Algebra 1
Practice B
Slopes of Parallel and Perpendicular Lines
Identify which lines are parallel.
1. y = 3x + 4; y = 4; y = 3x; y = 3
________________________________________________________________________________________
2. y =
1
2x + 4; x =
1
2; 2x + y = 1; y =
1
2x + 1
________________________________________________________________________________________
3. Find the slope of each segment.
slope of AB : ____________________________
slope of AD : ____________________________
slope of DC : ____________________________
slope of BC : ____________________________
Explain why ABCD is a parallelogram.
________________________________________________________________________________________
________________________________________________________________________________________
Identify which lines are perpendicular.
4. y = 5; y =
1
8x; x = 2; y = 8x 5
________________________________________________________________________________________
5. y = 2; y =
1
2x 4; y 4 = 2(x + 3); y = 2x
________________________________________________________________________________________
6. Show that ABC is a right triangle.
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
LESSON
5-8
Name ________________________________________ Date __________________ Class__________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
5-75 Holt McDougal Algebra 1
Practice A Transforming Linear Functions
Fill in each blank with translation, rotation, or reflection. 1. A __________________________________ is like a turn. 2. A __________________________________ is like a slide. 3. A __________________________________ is like a flip.
Graph f(x) and g(x). Then describe the transformation(s) from the graph of f(x) to the graph of g(x). 4. f(x) = x; g(x) = x + 5
__________________________________________
__________________________________________
__________________________________________
5. f(x) = 2x − 1; g(x) = 4x − 1
__________________________________________
__________________________________________
__________________________________________
6. f(x) = x; g(x) = 12
x − 7
__________________________________________
__________________________________________
__________________________________________
7. The cost of making a ceramic picture frame at a paint-your-own pottery store is $12, plus $5 per hour while you paint. The total cost for the frame that you spend x hours painting is f(x) = 5x + 12. a. How will the graph of this function change if the cost of the frame is raised to $15?
_____________________________________________________________________________________
b. How will the graph of this function change if the hourly charge is lowered to $4?
_____________________________________________________________________________________
LESSON
5-9
Name ________________________________________ Date __________________ Class__________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
5-76 Holt McDougal Algebra 1
Practice B Transforming Linear Functions
Graph f(x) and g(x). Then describe the transformation from the graph of f(x) to the graph of g(x). 1. f(x) = x; g(x) = x + 3
__________________________________________
__________________________________________
__________________________________________
2. f(x) = 13
x − 4; g(x) = 14
x − 4
__________________________________________
__________________________________________
__________________________________________
3. f(x) = x; g(x) = 2x − 5
__________________________________________
__________________________________________
__________________________________________
4. Graph f(x) = −3x + 1. Then reflect the graph of f(x) across the y-axis. Write a function g(x) to describe the new graph.
__________________________________________
5. The cost of hosting a party at a horse farm is a flat fee of $250, plus $5 per person. The total charge for a party of x people is f(x) = 5x + 250. How will the graph of this function change if the flat fee is lowered to $200? if the per-person rate is raised to $8?
_________________________________________________________
_________________________________________________________
_________________________________________________________
LESSON
5-9