5 6 Inverse Variation Vocabulary inverse variation 5

5 -6 Inverse Variation Vocabulary inverse variation

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 1 A: 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 1 B: 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 1 A Tell whether each relationship is an inverse variation, a direct variation, or neither. Explain. x y 2 40 4 20 8 10 The product xy is constant, so the relationship is an inverse variation, and k = 80.

5 -6 Inverse Variation Check It Out: Example 1 B Tell whether each relationship is an inverse variation, a direct variation, or neither. Explain. x 4 7 10 y 25 14 10 y The product xy is not constant. The quotient x is not constant. The relationship is neither an inverse variation nor a direct variation.

5 -6 Inverse Variation 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 Use xy = k. 4 y = 72 y = 18 6 y = 72 y = 12 8 y = 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.

5 -6 Inverse Variation 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. 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 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.

5 -6 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.

5 -6 Inverse Variation 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 y direct variation; x is constant; the graph passes through (0, 0)

5 -6 Inverse Variation Lesson Quiz: Part I Tell whether each relationship represents an inverse variation, a direct variation, or neither. Explain. 3. 1. neither 2. direct inverse

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. xy = 100, 000; $25, 000, $12, 5000, $10, 000