5-6 Inverse Variation
Warm Up
Find each product or quotient.
1. 3(12)
2. 6(75)
81
3.
3
55
4.
6
5. Solve 6x = 54.
5-6 Inverse Variation
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.
5-6 Inverse Variation
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.
5-6 Inverse Variation
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.
5-6 Inverse Variation
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
5-6 Inverse Variation
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