notes 25

Inverse Variation

*Notes 25

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.

Tell whether each relationship is an inverse variation, a direct variation or neither. Explain.

Additional Example 1A: Identifying an Inverse Variation

Find y/x for each pair. x 4 6 8

y 12 18 24

The data represents a direct variation where k = 3.

Tell whether each relationship is an inverse variation, a direct variation or neither. Explain.

Additional Example 1B: Identifying an Inverse Variation

Find the product xy.x 3 4 5

y 40 30 24

The data represents a inverse variation where k = 120.

3(40) = 120 4(30) = 120 5(24) = 120

Check It Out: Example 1A

x 2 4 8

y 40 20 10

Tell whether each relationship is an inverse variation, a direct variation, or neither. Explain.

Check It Out: Example 1B

x 4 7 10

y 25 14 10

Tell whether each relationship is an inverse variation, a direct variation, or neither. Explain.

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.

Additional Example 2: Application

Use xy = k.

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.

xy = k

4y = 72

y = 18

xy = k

6y = 72

y = 12

xy = k

8y = 72

y = 9

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 widths3, 4, and 6 inches.

Check It Out: Example 2

Tell whether each graph represents an inverse variation, a direct variation, or neither. Explain.

Additional Example 3: Identifying a Graph of an Inverse Variation

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.

Tell whether each graph represents an inverse variation, a direct variation, or neither. Explain.

Additional Example 3 Continued

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.

Check It Out: Example 3Tell whether the graph represents an inverse variation, a direct variation, or neither. Explain.

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