1. 4.1 Write Linear Equations in slope-intercept form
Essential Question:
You will write equations of lines.
How do you write an equation of a line in slope-intercept form?
You will learn how to
answer this question by using the
slope and y-intercept or two points
to write an equation of the line.

2. Use slope and y-intercept to write an equation
EXAMPLE 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.

3. Standardized Test Practice
EXAMPLE 2
Standardized Test Practice
Which equation represents the line shown? A
y = – x + 3 2 5 B C
y = – x + 1 D
y = 3x + = –
The slope of the line is
rise
run –2 5 2 .
The line crosses the y-axis at (0, 3). So, the y-intercept is 3.
y = mx + b
Write slope-intercept form. 2
y = – x + 3 5 2
Substitute – for m and 3 for b. 5

4. EXAMPLE 2
Standardized Test Practice
ANSWER
The correct answer is A. B D C A

5. GUIDED PRACTICE
for Examples 1 and 2
Write an equation of the line with the given slope and y-intercept.
1. Slope is 8; y-intercept is –7.
y = 8x – 7
ANSWER

6. GUIDED PRACTICE
for Examples 1 and 2
Write an equation of the line with the given slope and y-intercept.
2. Slope is ; y intercept is –3. 3 4
y = 3 4
x – 3
ANSWER

7. EXAMPLE 3
Write an equation of a line given two points
Write an equation of the line shown.

8. Write an equation of a line given two points
EXAMPLE 3
Write an equation of a line given two points
SOLUTION
STEP 1
Calculate the slope.
x2 – x1 3
3 – 0
y2 – y1 = m
–1 – (–5) 4
STEP 2
Write an equation of the line. The line crosses the y-axis at (0, –5). So, the y-intercept is –5.
y = mx + b
Write slope-intercept form.
y = x – 5 4 3
Substitute for m and 5 for b. 4 3

9. EXAMPLE 4
Write a linear function
Write an equation for the linear function f with the values f(0) = 5 and f(4) = 17.
SOLUTION
STEP 1
Write f(0) = 5 as (0, 5) and f (4) = 17 as (4, 17).
STEP 2
Calculate the slope of the line that
passes through (0, 5) and (4, 17).
x2 – x1
4 – 0
y2 – y1 = m
17 – 5 4 12 3

10. Write a linear function
EXAMPLE 4
Write a linear function
STEP 3
Write an equation of the line. The line crosses the y-axis at (0, 5). So, the y-intercept is 5.
y = mx + b
Write slope-intercept form.
y = 3x + 5
Substitute 3 for m and 5 for b.
ANSWER
The function is f(x) = 3x + 5.
• How does f (4) = 17 correspond
to the ordered pair (x, y )?

11. GUIDED PRACTICE
for Examples 3 and 4
3. Write an equation of the line shown. 2 1
x + 1
y =
ANSWER –

12. GUIDED 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 – 2 3 4
ANSWER

13. GUIDED 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 1 3
ANSWER –

14. EXAMPLE 5
Solve a multi-step problem
Recording Studio
A recording studio charges musicians an initial fee of $50 to record an album. Studio time costs an additional $35 per hour.
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.

15. EXAMPLE 5
Solve a multi-step problem
SOLUTION
The cost changes at a constant rate, so you can write an equation in slope-intercept form to model the total cost. a.

16. EXAMPLE 5
Solve a multi-step problem
STEP 1
Identify the rate of change and the starting value.
Rate of change, m: cost per hour
Starting value, b: initial fee
STEP 2
Write a verbal model. Then write the equation. C = t 35 + 50

17. Solve a multi-step problem
EXAMPLE 5
Solve a multi-step problem
Use unit analysis to check the equation.
CHECK
hour
dollars =
hours + dollars
dollars
The total cost C is given by the function C = 35t + 50 where t is the studio time (in hours).
ANSWER
b. Evaluate the function for t = 10.
C = 35(10) + 50 = 400
Substitute 10 for t and simplify.
ANSWER
The total cost for 10 hours of studio time is $400.

18. GUIDED 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 +75
ANSWER

19. GUIDED PRACTICE
for Example 5
Find the total cost of recording an album that takes 10 hours of studio time. b.
$475
ANSWER

20. Daily Homework Quiz
Write an equation of the line with a slope of –4 and a y-intercept of 1. 1.
ANSWER
y = –4x + 1
Write an equation of the line that passes through the given points.
(–9, 1), (0, –8) 2.
ANSWER
y = –x – 8
(–4, –6), (0, 6) 3.
ANSWER
y = 3x + 6

21. Daily Homework Quiz
Write an equation for the linear function f with f(0) = –4 and f(–1) = –9. 4.
ANSWER
y = 5x – 4
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.
ANSWER
C = 12.99g + 20 where C is total cost and g is the number of games; $97.94

22. Essential Question:
You will write equations of lines.
How do you write an equation of a line in slope-intercept form?
• An equation in slope-intercept
form, y = mx+ b, has slope m and
y-intercept b.
• Given two points on a graph, one
of which gives the y-intercept, you
can find the slope m and the
y-intercept b and substitute those
values into y = mx + b.
• You can write a function in
slope-intercept form given values
of f (0), x, and f (x).
To write an equation in slope intercept form, substitute the slope for m and the y-intercept for
b in the equation y = mx + b. In real-world situations, use the constant rate of change for m and the starting value for b.