1. 5-6 Inverse Variation Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. 5-6 Inverse Variation Warm Up Find each product or quotient. 1. 3(12)2. 6(75) 3. 4. 5. Solve 6x = 54. 36450 279 x = 9 81 3 55 6 1616

3. 5-6 Inverse Variation Problem of the Day The directions say to mix 2 cups of red paint for every 5 cups of white paint. Amos has 7 cups of red paint. How much white paint does he need? 17.5 cups

4. 5-6 Inverse Variation MA.7.G.1.5 Distinguish direct variation from other relationships, including inverse variation. Sunshine State Standards

5. 5-6 Inverse Variation Vocabulary inverse variation

6. 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.

7. 5-6 Inverse Variation 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 y121824 The data represents a direct variation where k = 3.

8. 5-6 Inverse Variation 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 y403024 The data represents a inverse variation where k = 120. 3(40) = 120 4(30) = 120 5(24) = 120

9. 5-6 Inverse Variation Check It Out: Example 1A x248 y402010 The product xy is constant, so the relationship is an inverse variation, and k = 80. Tell whether each relationship is an inverse variation, a direct variation, or neither. Explain.

10. 5-6 Inverse Variation Check It Out: Example 1B x4710 y251410 The product xy is not constant. The quotient is not constant. The relationship is neither an inverse variation nor a direct variation. Tell whether each relationship is an inverse variation, a direct variation, or neither. Explain. yxyx

11. 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. 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

12. 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 widths 3, 4, and 6 inches. Check It Out: Example 2 xy = 36; the pizza pans are 3 inches by 12 inches, 4 inches by 9 inches and 6 inches by 6 inches.

13. 5-6 Inverse Variation 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.

14. 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.

15. 5-6 Inverse Variation Check It Out: Example 3 direct variation; is constant; the graph passes through (0, 0) Tell whether the graph represents an inverse variation, a direct variation, or neither. Explain. yxyx 510 15 20 25 2 3 4 5 6 7 8 9 10 1 Field Trip Number of Chaperones Number of Students 0

16. 5-6 Inverse Variation Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

17. 5-6 Inverse Variation Lesson Quiz: Part I neither Tell whether each relationship represents an inverse variation, a direct variation, or neither. Explain. direct 1. 2. 3. inverse

18. 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

19. 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 x1084 y45

20. 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 x10205 y408020