4.1 write linear equations in slope-intercept form you will write equations of lines. essential...
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4.1 Write Linear Equations in slope-intercept form
• You will write equations of lines.
Essential Question:• How do you write an
equation of a line in slope-intercept form?
You will learn how toanswer this question by using theslope and y-intercept or two pointsto write an equation of the line.
Warm-Up ExercisesEXAMPLE 1 Use slope and y-intercept to write an equation
Write an equation of the line with a slope of –2 and a y-intercept of 5.
y = mx + b Write slope-intercept form.
y = –2x + 5 Substitute –2 for m and 5 for b.
Warm-Up ExercisesEXAMPLE 2 Standardized Test Practice
Which equation represents the line shown?
The line crosses the y-axis at (0, 3). So, the y-intercept is 3.
y = mx + b Write slope-intercept form.
2y = – x + 35
2Substitute – for m and 3 for b.5
= = –The slope of the line is riserun
–2 5
25
.
A y = – x + 325 B y = – x + 35
2
C y = – x + 125 D y = 3x +
25
Warm-Up ExercisesEXAMPLE 2 Standardized Test Practice
ANSWER
The correct answer is A. B DCA
Warm-Up ExercisesGUIDED PRACTICE for Examples 1 and 2
1. Slope is 8; y-intercept is –7.
Write an equation of the line with the given slope and y-intercept.
y = 8x – 7 ANSWER
Warm-Up ExercisesGUIDED PRACTICE for Examples 1 and 2
2. Slope is ; y intercept is –3. 34
Write an equation of the line with the given slope and y-intercept.
y = 34
x – 3ANSWER
Warm-Up ExercisesEXAMPLE 3 Write an equation of a line given two points
Write an equation of the line shown.
Warm-Up ExercisesWrite an equation of a line given two points
y = mx + b
y = x – 543
Substitute for m and 5 for b.43
STEP 1
Write an equation of the line. The line crosses the y-axis at (0, –5). So, the y-intercept is –5.
SOLUTION
x2 – x1 33 – 0y2 – y1=m =
–1 – (–5)=
4
Write slope-intercept form.
EXAMPLE 3
Calculate the slope.
STEP 2
Warm-Up Exercises
SOLUTION
Write a linear function
Write an equation for the linear function f with the values f(0) = 5 and f(4) = 17.
Calculate the slope of the line that passes through (0, 5) and (4, 17).
Write f(0) = 5 as (0, 5) and f (4) = 17 as (4, 17).
EXAMPLE 4
STEP 1
x2 – x1 4 – 0y2 – y1=m =
17 – 5= 4
12=3
STEP 2
Warm-Up Exercises
y = mx + b Write slope-intercept form.
y = 3x + 5 Substitute 3 for m and 5 for b.
Write an equation of the line. The line crosses the y-axis at (0, 5). So, the y-intercept is 5.
STEP 3
EXAMPLE 4 Write a linear function
ANSWER
The function is f(x) = 3x + 5.
• How does f (4) = 17 correspondto the ordered pair (x, y )?
Warm-Up ExercisesGUIDED PRACTICE for Examples 3 and 4
3. Write an equation of the line shown.
2 1 x + 1y =ANSWER –
Warm-Up ExercisesGUIDED PRACTICE for Examples 3 and 4
Write an equation for the linear function f with the given values.
4.
f(0) = –2, f(8) = 4
y = x – 234
ANSWER
Warm-Up ExercisesGUIDED PRACTICE for Examples 3 and 4
Write an equation for the linear function f with the given values.
5.
f(–3) = 6, f(0) = 5
y = x + 5 13ANSWER –
Warm-Up ExercisesEXAMPLE 5 Solve a multi-step problem
A recording studio charges musicians an initial fee of $50 to record an album. Studio time costs an additional $35 per hour.
Recording Studio
Write an equation that gives the total cost of an album as a function of studio time (in hours).
a.
Find the total cost of recording an album that takes 10 hours of studio time.
b.
Warm-Up Exercises
SOLUTION
EXAMPLE 5 Solve a multi-step problem
The cost changes at a constant rate, so you can write an equation in slope-intercept form to model the total cost.
a.
Warm-Up Exercises
Identify the rate of change and the starting value.
Write a verbal model. Then write the equation.
Rate of change, m: cost per hour
Starting value, b: initial fee
STEP 1
STEP 2
C = t35 + 50
EXAMPLE 5 Solve a multi-step problem
Warm-Up Exercises
Substitute 10 for t and simplify.
b. Evaluate the function for t = 10.
The total cost C is given by the function C = 35t + 50 where t is the studio time (in hours).
ANSWER
Use unit analysis to check the equation.CHECK
EXAMPLE 5 Solve a multi-step problem
C = 35(10) + 50 = 400
ANSWER
The total cost for 10 hours of studio time is $400.
hourdollars = hours + dollarsdollars
Warm-Up ExercisesGUIDED PRACTICE for Example 5
WHAT IF? In Example 5, suppose the recording studio raises its initial fee to $75 and charges $40 per hour for studio time.
6.
Write an equation that gives the total cost of an album as a function of studio time (in hours).
a.
C = 40t +75ANSWER
Warm-Up ExercisesGUIDED PRACTICE for Example 5
Find the total cost of recording an album that takes 10 hours of studio time.
b.
$475ANSWER
Warm-Up ExercisesDaily Homework Quiz
ANSWER y = –4x + 1
Write an equation of the line with a slope of –4 and a y-intercept of 1.
1.
Write an equation of the line that passes through the given points.
(–9, 1), (0, –8)2.
ANSWER y = –x – 8
ANSWER y = 3x + 6
(–4, –6), (0, 6)3.
Warm-Up ExercisesDaily Homework Quiz
An electronics game store sells used games for $12.99 with a $20 membership fee. Write an equation that gives the total cost to become a member and buy games as a function of the number of games that are purchased. Then find the cost for 6 games.
5.
Write an equation for the linear function f with f(0) = –4 and f(–1) = –9.
4.
ANSWER y = 5x – 4
ANSWERC = 12.99g + 20 where C is total cost and g is the number of games; $97.94
• You will write equations of lines.
Essential Question:
• How do you write an equation of a line in slope-intercept form?
• An equation in slope-interceptform, y = mx+ b, has slope m andy-intercept b.• Given two points on a graph, oneof which gives the y-intercept, youcan find the slope m and they-intercept b and substitute thosevalues into y = mx + b.• You can write a function inslope-intercept form given valuesof f (0), x, and f (x).
To write an equation in slope intercept form, substitute the slope for m and the y-intercept forb in the equation y = mx + b. In real-world situations, use the constant rate of change for m and the starting value for b.