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Name
LESSON
Date
Class
Reteach
11-3 Using Slopes and Intercepts
x-intercept: the x-coordinate of the point
at which a line crosses the x-axis
y
y-intercept: the y-coordinate of the point
at which a line crosses the y-axis
(0, y-intercept)
You can find the intercepts of a line from its equation.
Then you can use the intercepts to graph the line.
(x-intercept, 0)
For the x-intercept,
let y 0.
For the y-intercept,
let x 0.
3x 4y 24
3x 4(0) 24
3x 0 24
3x 24
3x 4y 24
3(0) 4y 24
0 4y 24
4y 24
3x
24
3
3
4y
24
4
4
x8
The x-intercept is 8.
x
O
Find the intercepts of the line 3x 4y 24.
y
8
3x 4y 24
4
x
8
O
4
4
8
4
y6
The y-intercept is 6.
8
Find the intercepts of each line.
Draw both graphs on the same grid.
1. 2x 3y 12
for x-intercept
2x 3(
) 12
for y-intercept
2(
) 3y 12
y
8
x
2. 6y 3x 6
for x-intercept
6(
) 3x 6
y
4
x
for y-intercept
6y 3(
)6
8
4
O
4
8
4
8
x
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
y
32
Holt Pre-Algebra
Holt Middle
School Math
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Name
Date
LESSON
Class
Reteach
11-3 Using Slopes and Intercepts (continued)
To put an equation in slope-intercept
form, isolate y.
slope-intercept form
y mx b
slope
2x 3y 12
2x
2x
y-intercept
Subtract 2x
3y 2x 12
In this form, the coefficient of x is
the slope and the constant term
is the y-intercept.
3y
2
12
x Divide by 3.
3
3
3
2
y 3x 4
2
So, m 3 and b 4.
Identify the slope and y-intercept of each line.
3. 3y 4x 15
3y
4
15
x 4. 3x 2y 6
Work to isolate y.
Divide to isolate y.
y
slope m y-intercept b m
b
Given information about a line, you can write its equation.
Write an equation of the line that passes
y mx b
2
2
through (3, 5) and has slope 3.
5 3(3) b
2
Given m 3 and (x, y) (3, 5).
52b
2
Use this information to find b.
slope-intercept form
Substitute for m, x, y.
Solve for b.
2
3b
2
y 3x 3
equation of line
5. Write an equation of the line that
passes through (10, 4) and has
3
slope 5.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
6. Substitute for m, x, y, and solve for b.
3
Use point (10, 4) and slope 5.
y mx b
33
Holt Pre-Algebra
Holt Middle
School Math