5-6 Inverse Variation

Inverse variation is a relationship between two variables that can be written in the form

y = or xy = k, where k is a nonzero

constant and x 0.

In an inverse variation, the product of x and y is constant.

kx

5-6 Inverse Variation

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

x 3 4 5

y 40 30 24

5-6 Inverse Variation

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

x 4 6 8

y 12 18 24

5-6 Inverse Variation

x 2 4 8

y 40 20 10

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

5-6 Inverse Variation

x 4 7 10

y 25 14 10

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

5-6 Inverse Variation

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.

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

5-6 Inverse Variation

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.

xy = 36; the pizza pans are 3 inches by 12 inches, 4 inches by 9 inches and 6 inches by 6 inches.

5-6 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.

5-6 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.

5-6 Inverse Variation

direct variation; is constant; the graph passes through (0, 0)

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

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5-6 Inverse Variation

Lesson Quiz: Part I

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

1.

2.

3.

5-6 Inverse Variation

Lesson Quiz: Part II

4. A company will donate $100,000 to local schools. Write an inverse variation equation to represent the money that will be donated. Use the equation to find the amount of money donated for 4, 8, and 10 schools.

5-6 Inverse Variation

1. Tell whether each relationship represents an inverse variation, a direct variation, or neither.

A. inverse

B. direct

C. neither

Lesson Quiz for Student Response Systems

x 10 8 4

y 4 5 10

5-6 Inverse Variation

2. Tell whether each relationship represents an inverse variation, a direct variation, or neither.

A. inverse

B. direct

C. neither

Lesson Quiz for Student Response Systems

x 10 20 5

y 40 80 20