NAME
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4-1
DATE
PERIOD
Study Guide and Intervention
Graphing Equations in Slope-Intercept Form
Slope-Intercept
Form
y = mx + b, where m is the given slope and b is the y-intercept
Slope-Intercept Form
Example 1
Write an equation in slope-intercept form for the line with a slope
-4 and a y-intercept of 3.
of
Slope-intercept form
y
= mx + b
y
= -4x + 3
Replace m with -4 and b with 3.
Example 2
y
Graph 3x - 4y = 8.
(4, 1)
Original equation
3x
- 4y = 8
O
x
Subtract 3x from each side.
-4y = -3x + 8
(0, –2)
-4y
-3x + 8
−
3x - 4y = 8
=−
Divide each side by -4.
-4
-4
3
y=−
x-2
Simplify.
4
3
3
The
y-intercept of y = − x - 2 is -2 and the slope is −
. So graph the point (0, -2). From
4
this point, move up 3 units and right 4 units. Draw a4 line passing through both points.
Exercises
Write an equation of a line in slope-intercept form with the given slope and
y-intercept.
1. slope: 8, y-intercept -3
2. slope: -2, y-intercept -1
3. slope: -1, y-intercept -7
Write
an equation in slope-intercept form for each graph shown.
y
y
y
5.
6.
4.
x
(0, 3)
O
(4, –2)
O
x
(1, 0)
O
x
(3, 0)
(0, –2)
(0, –5)
Graph
each equation.
7. y = 2x + 1
8. y = -3x + 2
9. y = -x - 1
y
y
y
O
O
x
x
O
x
Chapter 4
47
Glencoe Algebra 1
NAME
DATE
2-4
PERIOD
Study Guide and Intervention
Solving Equations with the Variable on Each Side
Variables
on Each Side To solve an equation with the same variable on each side,
first
use the Addition or the Subtraction Property of Equality to write an equivalent
equation
that has the variable on just one side of the equation. Then solve the equation.
Example 1
5y - 8
5y - 8 - 3y
2y - 8
2y - 8 + 8
2y
Example 2
Solve 5y - 8 = 3y + 12.
=
=
=
=
=
-11 - 3y = 8y + 1
-11 - 3y + 3y = 8y + 1 + 3y
-11 = 11y + 1
-11 - 1 = 11y + 1 - 1
-12 = 11y
3y + 12
3y + 12 - 3y
12
12 + 8
20
11y
11
11
1
-1− = y
11
2y
20
−=−
-12 = −
−
2
2
Solve -11 - 3y = 8y + 1.
y = 10
The solution is 10.
1
The solution is -1 −
.
11
Exercises
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Solve each equation. Check your solution.
1. 6 - b = 5b + 30
2. 5y - 2y = 3y + 2
3. 5x + 2 = 2x - 10
4. 4n - 8 = 3n + 2
5. 1.2x + 4.3 = 2.1 - x
6. 4.4m + 6.2 = 8.8m - 1.8
1
1
7. −
b+4=−
b + 88
3
1
8. −
k-5=−
k-1
9. 8 - 5p = 4p - 1
2
8
4
4
10. 4b - 8 = 10 - 2b
11. 0.2x - 8 = -2 - x
12. 3y - 1.8 = 3y - 1.8
13. -4 - 3x = 7x - 6
14. 8 + 4k = -10 + k
15. 20 - a = 10a - 2
2
1
16. −
n+8=−
n+2
3
2
17. −
y-8=9-−
y
18. -4r + 5 = 5 - 4r
19. -4 - 3x = 6x - 6
20. 18 - 4k = -10 -4k
21. 12 + 2y = 10y - 12
3
Chapter 2
2
5
5
23
Glencoe Algebra 1