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Warm Up

Warm Up. Problem of the Day. Lesson Presentation. Lesson Quizzes. Warm Up Find each product or quotient. 1. 3(12) 2. 6(75) 3. 4. 5. Solve 6 x = 54. 36. 450. 81 3. 55 6. 1 6. 27. 9. x = 9. Problem of the Day

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Warm Up

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  1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

  2. Warm Up Find each product or quotient. 1. 3(12) 2. 6(75) 3.4. 5. Solve 6x = 54. 36 450 81 3 55 6 1 6 27 9 x = 9

  3. 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. Sunshine State Standards MA.7.G.1.5 Distinguish direct variation from other relationships, including inverse variation.

  5. Vocabulary inverse variation

  6. 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. Additional Example 1A: Identifying an Inverse Variation Tell whether each relationship is an inverse variation, a direct variation or neither. Explain. Find y/x for each pair. The data represents a direct variation where k = 3.

  8. Additional Example 1B: Identifying an Inverse Variation Tell whether each relationship is an inverse variation, a direct variation or neither. Explain. Find the product xy. 3(40) = 120 4(30) = 120 5(24) = 120 The data represents a inverse variation where k = 120.

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

  10. Check It Out: Example 1B Tell whether each relationship is an inverse variation, a direct variation, or neither. Explain. y x The product xy is not constant. The quotient is not constant. Therelationship is neither an inverse variation nor a direct variation.

  11. 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 xy = k xy = k Use xy = k. 4y = 72 6y = 72 8y = 72 Substitute for x and k. y = 18 y = 12 y = 9 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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 Number of Chaperones 6 5 4 3 2 1 0 15 5 10 20 25 Number of Students y x direct variation; is constant; the graph passes through (0, 0)

  16. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

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

  18. 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. Lesson Quiz for Student Response Systems 1. Tell whether each relationship represents an inverse variation, a direct variation, or neither. A. inverse B. direct C. neither

  20. Lesson Quiz for Student Response Systems 2. Tell whether each relationship represents an inverse variation, a direct variation, or neither. A. inverse B. direct C. neither

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