Name
Date
Class
Reteach
LESSON
5-5
Direct Variation
A direct variation is a special type of linear relationship. It can be written
in the form y  kx where k is a nonzero constant called the constant of variation.
You can identify direct variations from equations or from ordered pairs.
Tell whether 2x  4y  0 is a direct
variation. If so, identify the constant of
variation.
Tell whether the relationship is a direct
variation. If so, identify the constant of
variation.
First, put the equation in the form y  kx.
2x  4y  0
2x
Add 2x to each side.
2x
_
x
2
4
6
y
1
2
3
If we solve y  kx for k, we get:
y __
y
kx
__
__
y  kx
x x
xk
Find k for each ordered pair. This means
y
find __
x for each ordered pair. If they are the
same, the relationship is a direct variation.
4y  2x
4y
2x
___
 ___
Divide both sides by 4.
4
1x
y  __
2
Because the equation can be written in the
form y  kx, it is a direct variation.
1.
The constant of variation is __
2
4
1
__
3  __
1
__
2  __
1
__
2
4
2
6
2
This is a direct variation.
Tell whether each equation or relationship is a direct variation. If so,
identify the constant of variation.
1. x  y  7
4.
x
4
y
2
2. 4x  3y  0
2
10
1 5
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a107c05-5_rt.indd 38
5.
3. 8y  24x
x
5
12
8
y
17.5
42
28
38
6.
x
6
8
10
y
8
10
12
Holt Algebra 1
12/12/05 7:54:43 PM
Name
LESSON
5-5
Date
Class
Reteach
Direct Variation (continued)
If you know one ordered pair that satisfies a direct variation, you can find
and graph other ordered pairs that will also satisfy the direct variation.
The value of y varies directly with x,
and y  8 when x  24. Find y when
x  27.
A garden snail can travel about 2.6
feet per minute. Write a direct variation
equation for the distance y a snail will
travel in x minutes. Then graph.
We have to find how the y varies with the
change in x. Then we can find the value of y
when x  27.
y  kx
Use the equation for direct
variation.
8  k  24 
Substitute 8 for y and 24 for x
24
24
Simplify.
1x
y  __
3
Write the direct variation
equation.
1  27 
y  __
3
y  2.6x
Step 2: Generate ordered pairs.
Solve for k.
1k
__
3
distance  2.6 feet  minutes
x
y  2.6x
0
y  2.6  0 
1
y  2.6  1 
2
y  2.6  2 
 x, y 
 0, 0 
 1, 2.6 
 2, 5.2 
����������������
Step 3: Graph.
��
�
�
Substitute 27 for x.
�������������
k  24 
8  _____
___
Step 1: Write an equation.
y9
�
�
�
�
�
�
�
�
�
�
�
�
����������
7. The value of y varies directly with x, and y  8 when x  2.
Find y when x  10.
8. The value of y varies directly with x, and y  5 when x  20.
Find y when x  35.
�
9. The cost of electricity to run a personal computer is
about $2.13 per day. Write a direct variation equation
for the electrical cost y of running a computer each
day x. Then graph.
��
�
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�
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����
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a107c05-5_rt.indd 39
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