Name
_
Date
_
C Direct Variation
When the ratio of two variables is constant, they show direct variation. In a direct
variation, when one variable increases the other variable increases proportionally.
Similarly, when one variable decreases the other variable decreases proportionally.
Rules for Direct Variation
1. Examine the data. When one variable varies does the other variable vary in proportion?
2. Does the ratio of the two variables stay constant?
3. Does the graph of the data go through the origin?
4. If the answer is "yes" to all questions, then the data show a direct variation.
Example
Tell whether the data show a direct variation.
120
3
4
280
160
Time (hours)
1
40
Step 1 Examine the data. When one variable
Yes,as hours increase, the distance increases.
varies does the other variable vary in
proportion?
. 0 f distance·
80
Step 2 Does the ratio of the two variables stay Yies, the ratlO
t'lme IS 40 (e.g. -2
constant?
Step 3 Does the graph of the data go through
= 40) .
Yes, the graph does go through the origin.
the origin?
Step 4 If the answer is "yes" to all questions,
then the data show a direct variation.
Practice
Each question was answered "yes:' so the data
show a direct variation.
A
Tell whether the data show a direct variation.
1.
80
5.0
3.5
55
40
2.0
0.5
30
Time (hours)
Step 1 As the time increases the distance
Step 2 The ratio of dis.tance
tlme
-----Step 3 The graph
Step 4 The data
2.
3.
_
40
45
36
50
27
30
20
18
Drop Height (em)
4
75
60
5
45
32
30
Age (months)
,
constant.
go through the origin.
show a direct variation.
910
1
15
Algebra 2
16
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Name
_
Date
_
C Inverse Variation
When you have a set of data in which one variable increases while the other decreases
and the product of the variables is constant, you have an inverse variation.
Rules for an Inverse Variation.
1. Examine the data. Does one variable increase while the other one decreases?
2. Is the product xya constant value?
3. If the answers to both 1 and 2 are "yes," the data show an inverse variation.
Example
Do the data in the table represent an inverse variation?
12
26
68
43
x
Y
Step 1 Examine the data. Does one variable
increase while the other one decreases?
Step 2 Is the product xya constant value?
Yes,as the value for x increases, the value for y
decreases.
Yes,the product of xy is the same value, 24.
For example, 2 x 12 = 24; 4 x 6 = 24.
Step 3 If the answers to both 1 and 2 are "yes," The answers to both are yes. The data show
the data show an inverse variation.
Practice
an inverse variation.
:B
Do the data in the table below represent an inverse variation?
1.
34961
36
x 12
Examine the data. Does one variable
increase while the other one decreases?
As the value for x decreases, the value for y
Is the product xya constant value?
The product xy
a constant. For
example, 9 x 4 =
If the answers to both 1 and 2 are "yes,"
the data show an inverse variation.
The answer to question 1 is
answer to question 2 is
___
2.
_
4
20
862
16
10
x 12
;6 x 6 =
.
, the
; the data
show an inverse variation.
4.
_
18
4
612
839
x 24
Y
3.
_
x
15
45
12
20
3230
Y
Algebra 2
78
Saddle back Educational Publishing ©2006 • (888) 735-2225 • www.sdlback.com