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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 1 Tell whether each relationship is an inverse variation, a direct variation or neither. Explain. 6(5) = 30 8(32) = 256 12(36) = 432 The relationship is neither.

10. 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.

11. Check It Out: Example 2 Erik has to drive 200 miles to get to a friend’s birthday party. He wants to know how fast he must drive to make it there in 4, 5, or 8 hours. For each x, find the number of miles per hour he must drive y to get there. xy = k xy = k xy = k Use xy = k. 4y = 200 5y = 200 8y = 200 Substitute for x and k. y = 50 y = 40 y = 25 To make it to the party in 4 hours, Erik must drive 50 mi/h, to make it in 5 hours, he must drive 40 mi/h, and to make it in 8 hours, he must drive 25 mi/h.

12. 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.

13. 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.

14. Check It Out: Example 3 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)–1 = 1 (–2)–4 = 8, (2)–4 = –8 The values of k are not constant. The graph does not represent an inverse variation.

15. Check It Out: 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. 2/–4 = –2,–2/–4 = 2 The values of k are not constant. The graph does not represent an direct variation. The graph is neither.

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 neither

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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