LESSON
Direct Variation
12-5
Lesson Objectives
Recognize direct variation by graphing tables of data and checking for constant
ratios.
Vocabulary
direct variation (p. 650)
constant of proportionality (p. 650)
Additional Examples
Example 1
Determine whether the data set shows direct variation.
Adam’s Growth Chart
Age (mo)
Length (in.)
28
3
6
9
12
22
24
25
27
Make a graph that shows the
relationship between Adam’s age
and his length.
Length (in)
A.
26
24
22
20
0
0
3
6
9
12
15
Age (mo)
You can also compare ratios to see if a direct
81
⎯
? ⎯
22⎯⎯
27⎯→
⎯⎯
⎯
⎯
3
12 →
⎯
264
The ratios are
.
The relationship of the data is
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
occurs.
.
248
Holt Mathematics
LESSON
Direct Variation
12-5
Lesson Objectives
Recognize direct variation by graphing tables of data and checking for constant
ratios.
Vocabulary
direct variation (p. 650) A relationship between two variables in which the data
increase or decrease together at a constant rate.
constant of proportionality (p. 650) A constant ratio of two variables related
proportionally.
Additional Examples
Example 1
Determine whether the data set shows direct variation.
Adam’s Growth Chart
Age (mo)
Length (in.)
28
3
6
9
12
22
24
25
27
Make a graph that shows the
relationship between Adam’s age
and his length.
Length (in)
A.
26
24
22
20
0
0
3
6
9
12
15
Age (mo)
You can also compare ratios to see if a direct variation
81
⎯
? ⎯
22⎯⎯
27⎯→
⎯⎯
⎯
⎯
3
12 →
⎯
264
81
264
The ratios are not proportional
The relationship of the data is not a direct variation
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
occurs.
248
.
.
Holt Mathematics
LESSON 12-5 CONTINUED
Example 2
Find each equation of direct variation, given that y varies directly with x.
A. y is 54 when x is 6
y kx
k
k
y varies
with x.
Substitute for x and y.
Solve for k.
y
Substitute
for k in the original equation.
B. x is 12 when y is 15
y kx
k
k
y
y varies
with x.
Substitute for x and y.
Solve for k.
Substitute
for k in the original equation.
Try This
Kyle’s Basketball Shots
1. Determine whether the data set
shows direct variation.
Distance (ft)
Number of Baskets
20
30
40
5
3
0
2. Find the equation of direct variation, given that y varies directly with x.
y is 7 when x is 3
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
249
Holt Mathematics
LESSON 12-5 CONTINUED
Example 2
Find each equation of direct variation, given that y varies directly with x.
A. y is 54 when x is 6
y varies directly
y kx
54
k
9
6
k
with x.
Substitute for x and y.
Solve for k.
y 9x
Substitute 9
for k in the original equation.
B. x is 12 when y is 15
y varies directly
y kx
15
k
5
4
12
k
with x.
Substitute for x and y.
Solve for k.
5
x
y 4
5
Substitute 4
for k in the original equation.
Try This
Kyle’s Basketball Shots
1. Determine whether the data set
shows direct variation.
Distance (ft)
Number of Baskets
20
30
40
5
3
0
not a direct variation
2. Find the equation of direct variation, given that y varies directly with x.
y is 7 when x is 3
7
y 3x
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
249
Holt Mathematics