5-3 Equations in Slope-Intercept Form
Name
Date
3
Given the equation y 4 x 2, identify the slope and y-intercept.
Then graph the line.
3
Plot the y-intercept, (0, 2).
y 4x 2
y
4
Think
The slope-intercept form of a linear
equation is y mx b, where m is
the slope and b is the y-intercept.
3
So the slope (m) 4 , and the
y-intercept (b) 2.
Remember: The ordered pair
for the y-intercept of a line is
always (0, b).
2
m 3 vertical change
4 horizontal change
x
4
2
Count 3 units up and 4 units
to the right from (0, 2) to plot
another point.
0
2
4
2
4
Draw the line
through both points.
Write an equation in slope-intercept form for the line with the given slope and y-intercept.
1. slope: 4; y-intercept: 9
2. slope: 2; y-intercept: 5
y mx b
m 4; b 9
y 4x 9
11
17
Copyright © by William H. Sadlier, Inc. All rights reserved.
11
17
x
9
5
5. slope: 2.5; y-intercept: 7.9
3
7
3
y x
2
5
y 2x 5
4. slope: 9 ; y-intercept: 5
y
7
3. slope: 2 ; y-intercept: 5
6. slope: 5.3; y-intercept: 4.1
y 2.5x 7.9
y 5.3x 4.1
Identify the slope and y-intercept of the line whose equation is given.
Graph the equation on a separate sheet of paper. Check students’ graphs.
7. y x 8
slope (m) 1
y-intercept (b) 8
10. 5x 2y 12
2y 5x 12
5
y x6
2
5
slope ; y-intercept 6
2
13. 2x 8y 0
8y 2x
1
y x
4
1
slope ; y-intercept 0
4
8. y x 12
slope 1
y-intercept 12
11. 2x 10
x 5
slope undefined
no y-intercept
14. 5x y 0
y 5x
slope 5
y-intercept 0
Lesson 5-3, pages 122–125.
9. 5y 2x 15
5y 2x 15
2
y x3
5
2
slope ; y-intercept 3
5
12. 5y 25
y 5; y 0x – 5
slope 0
y-intercept 5
15. 1.4x 0.7y 2 0.1
0.7y 2.1 1.4x
y 3 2x
slope 2
y-intercept 3
Chapter 5
115
For More Practice Go To:
Write the slope-intercept form of the equation of the line shown.
16.
y
2
0
x
2
17.
4
2
y
4
x
2
0
2
4
2
4
y mx b
slope (m) 5
y-intercept (b) 5
y 5x 5
18.
y
2
x
4
0
4
8
4
7
m ; b 4
5
7
y x4
5
4
m ;b1
3
4
y x1
3
Write an equation in slope-intercept form with the given slope and containing the given point.
19. slope 9; (2, 8)
y mx b; 8 (9)(2) b
8 18 b; 26 b
y 9x 26
2
20. slope 9 ; (5, 2)
2
y mx b; 2 (5) b
9
28
10
b
b;
2 9
9
28
2
y x
9
9
21. slope 3.5; (2.8, 2.9)
y mx b; 2.9 3.5(2.8) b
2.9 9.8 b; 12.7 b
y 3.5x 12.7
Solve. Show your work.
y 22x 45
24. Traveling Ava is driving at a constant rate.
3
After 3 4 h of travel, she is 291.25 miles from
1
home. After 5 2 h of travel, she is 422.5 miles
from home. How many miles from home was
she when she began driving?
23. Janice can install 8 fence posts per hour.
Write an equation in slope-intercept form
that represents how many fence posts Janice
can install.
y 8x
25. Celine makes $10.75 per hour at her parttime job. If she wants to buy a pair of jeans
for $22.75, a blouse for $35.95, and boots for
$51.95, but owes her parents $33.25, how
many complete hours must she first work?
7
26. Explain how to find the equation of a line with slope 2 that passes
through the point (5, 1).
7
Possible response: Substitute for the slope, x 5, and y 1 in the slope-intercept form of a
2
7
35
33
line, and solve for the y-intercept b. y mx b
1 (5) b, 1 b, b. Then
2
2
2
7
33
7
33
substitute for the slope and for the y-intercept into the slope-intercept form. y x 2
2
2
2
( )
116
Chapter 5
Copyright © by William H. Sadlier, Inc. All rights reserved.
22. Wu earns $22 per hour plus a set-up fee of
$45 to paint houses. Write an equation in
slope-intercept form that represents how
much Wu earns for painting houses.
Answers for Algebra 1, Practice Book Lesson 5-3, page 116.
24. If Ava has been driving at a constant rate, you can model Ava’s trip using the
slope-intercept form. To find where she began driving, find b, the y intercept.
422.5 75(5.5) b; b 10
m 422.5 291.25 131.25 75; y mx b
7
11 15
4
2
4
Ava began driving 10 mi from home.
25. You can represent this situation by using the slope-intercept form, where
y what Celine wants to buy; x number of hours Celine must first work;
b amount Celine owes her parents; m Celine’s hourly rate.
(22.75 35.95 51.95) 10.75x 33.25; 110.65 10.75x 33.25
143.9 10.75x; 13.38. . . x
Celine must first work 14 hours.
116A
Chapter 5