e x p l o r at i o n
Georgia Performance
Standards
12E Direct Variation
M8A3.h, M8A3.i,
M8A4.f, M8A4.g
In a direct variation, when one quantity increases or decreases,
the other quantity does the same. The table below shows the
number of stamps x and the price y for each number.
Notice that when the number of stamps is doubled, the price is
also doubled.
2
$0.74
3
$1.11
1. Use each pair of values (x, y)
in the table to complete
the graph.
2. To find the constant of
proportionality, divide each
price in the table by each
number of stamps.
3. What feature of the graph
tells you that the graph is of
a direct variation?
4
$1.48
5
$1.85
6
$2.22
2.22
1.85
Price ($)
Stamps x
1
Price y
$0.37
1.48
1.11
0.74
0.37
0
1
2
3
4
5
6
Number of stamps
Think and Discuss
4. Explain the relationship between a constant of
proportionality and the slope of the line.
5. Give a real-world example of a direct variation.
Copyright © by Holt, Rinehart and Winston.
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396
Holt Mathematics
Name
Date
Class
Review for Mastery
LESSON
12E Direct Variation
Two data sets have direct variation if they are related by a constant
ratio, the constant of proportionality. A graph of the data sets is
linear and passes through (0, 0).
y
y kx equation of direct variation,
where k is the constant ratio
40
30
To determine whether two data sets have direct
variation, you can compare ratios. You can also
graph the data sets on a coordinate grid.
x
3
5
8
y
15
25
40
20
10
x
2
y
15
25
40
5
x
3
5
8
1
4
6
8
constant ratio
k 5 → y 5x
The graph of the data sets is linear and passes through (0, 0).
So, the data sets show direct variation.
Determine whether the data sets show direct variation. If there
is a constant ratio, identify it and write the equation of direct
variation. Plot the points and tell whether the graph is linear.
1.
2.
x
1
2
4
8
x
0
2
y
8
4
2
1
y
0
20
constant ratio?
constant ratio?
If yes, equation.
If yes, equation.
Is the graph linear?
Is the graph linear?
3
5
30
50
y
y
8
50
6
40
4
30
2
20
x
2
4
6
8
10
x
2
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
397
4
6
Holt Mathematics
Name
LESSON
Date
Class
Homework and Practice
12E Direct Variation
Make a graph to determine whether the data set shows direct
variation.
1.
y
x
y
4
3
6
8
6
4
0
0
4
3
2
x
6
4 2 O
2
4
6
2
4
2. Write the equation of direct variation
for exercise 1.
6
Find each equation of direct variation, given that y varies
directly with x.
3. y is 27 when x is 3
4. y is 8 when x is 40
5. y is 54 when x is 12
6. y is 21 when x is 49
7. y is 31.5 when x is 14
8. y is 180 when x is 216
9. Bridgett’s gross pay per year is $40,300. Her net pay is $27,001
as a result of her payroll deductions. Last year Bridgett’s gross
salary was $37,700. Her net pay was $25,259. Write an equation
of direct variation indicating Bridgett’s gross pay, x, versus her
net pay, y.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
398
Holt Mathematics