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.

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. x468 y 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. x345 y The data represents a inverse variation where k = (40) = 120 4(30) = 120 5(24) = 120

Check It Out: Example 1A x248 y Tell whether each relationship is an inverse variation, a direct variation, or neither. Explain.

Check It Out: Example 1B x4710 y 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 widths 3, 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 3 Tell whether the graph represents an inverse variation, a direct variation, or neither. Explain Field Trip Number of Chaperones Number of Students 0