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Inverse Variation
Vocabulary
Inverse variation- a relationship
between two variables that can be
written in the form y =k/x or xy = k,
where k is a nonzero constant and x
 0.
Inverse variation is a relationship between two
variables that can be written in the form y =k/x or
xy = k, where k is a nonzero constant and x  0.
In an inverse variation, the product of x and y is
constant.
Additional Example 1A: Identifying an Inverse
Variation
Tell whether each relationship is an inverse
variation, a direct variation or neither.
Explain.
x
y
4
12
6
18
8
24
Find y/x for each pair.
The data represents a direct variation where k = 3.
Additional Example 1B: Identifying an Inverse
Variation
Tell whether each relationship is an inverse
variation, a direct variation or neither.
Explain.
x
y
3
40
4
30
3(40) = 120
5
24
Find the product xy.
4(30) = 120
5(24) = 120
The data represents a inverse variation where
k = 120.
Check It Out: Example 1A
Tell whether each relationship is an inverse
variation, a direct variation, or neither.
Explain.
x
y
2
40
4
20
8
10
Check It Out: Example 1B
Tell whether each relationship is an inverse
variation, a direct variation, or neither.
Explain.
x
4
7
10
y
25
14
10
Additional Example 2: Application
Eliza is building a rectangular patio. She has
cement to cover 72 square feet. Write an
inverse variation equation to find the width of
the patio for lengths 4, 6, and 8 feet.
xy = k
xy = k
xy = k
Use xy = k.
4y = 72
y = 18
6y = 72
y = 12
8y = 72
y=9
Substitute
for x and k.
An inverse variation equation is xy = 72. Eliza can
build a 4 ft by 18 ft, 6 ft by 12 ft, or 8 ft by 9 ft patio.
Check It Out: Example 2
A pizzeria makes rectangular pizzas. One ball
of dough can cover 36 square inches.
Write an inverse variation equation to
represent the length of the pans for widths
3, 4, and 6 inches.
Additional Example 3: Identifying a Graph of an
Inverse Variation
Tell whether each graph represents an inverse
variation, a direct variation, or neither.
Explain.
Identify points on the graph. Use
the equation xy = k.
(1)2= 2, (2)3 = 6
The values of k are not constant.
The graph does not represent an
inverse variation.
Additional Example 3 Continued
Tell whether each graph represents an inverse
variation, a direct variation, or neither.
Explain.
Identify points on the graph. Use
the equation y/x = k.
1/1 = 1, 2/1 = 2
The values of k are not constant.
The graph does not represent an
direct variation.
The graph is neither.
Number of
Chaperones
Check It Out: Example 3
Tell whether the graph represents an inverse
variation, a direct variation, or neither.
Explain.
Field Trip
10
9
8
7
6
5
4
3
2
1
0
5
10
15
20
25
Number of Students