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Math on the Mind

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Explore the concepts of direct and inverse variation in algebra through engaging examples and exercises. Learn to identify if equations exhibit direct variation, calculate the constant of variation, and formulate equations based on given points. Follow Mrs. King's cookie distribution scenario to understand how the number of items per student changes with varying attendance. This guide also includes practical worksheets to reinforce learning. Perfect for students seeking to master variation concepts in mathematics.

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Math on the Mind

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  1. 8 3 xy –1 –2 0 0 1 2 3 –6 xy –1 3 0 0 2 –6 3 –9 b. a. yes; – 4 5 y = x Math on the Mind 1. Is each equation a direct variation? If it is, find the constant of variation. a.x + 5y = 10 b. 3y + 8x = 0 no 2. Write an equation of the direct variation that includes the point (–5, –4). 3. For each table, tell whether y varies directly with x. If it does, write an equation for the direct variation. yes; y = –3x no

  2. Inverse Variation Mrs. King Algebra A Unit 7, Day 2

  3. Party Time! • Mrs. King baked cookies for her students. She has 12 students in her class, so she baked 24 cookies. • If all students are present, how many cookies does each student get?

  4. Party Time! • Mrs. King baked cookies for her students. She has 12 students in her class, so she baked 24 cookies. • A nasty cold leaves 4 students home in bed. If only 8 students are present, how many cookies does each student get?

  5. Party Time! • Mrs. King baked cookies for her students. She has 12 students in her class, so she baked 24 cookies. • 4 new students join the class. If now 16 students are present, how many cookies does each student get?

  6. Evaluating results • What happens to the number of cookies per student as the number of students increases?

  7. Vocabulary: • Inverse Variation: a function in the form xy = k or

  8. Writing the equation of an inverse variation http://www.phschool.com/atschool/academy123/english/academy123_content/wl-book-demo/ph-197s.html

  9. Suppose y varies inversely with x, and a point on the graph of the equation is (8, 9). Write an equation for the inverse variation. xy = k (8)(9) = k 72 = k xy = 72

  10. xy = k (5)(7) = k 35 = k xy = 35 Suppose y varies inversely with x and y=7 when x=5. Write an equation for the inverse variation.

  11. xy = k (2)(9) = k 18 = k xy = 18 Suppose y varies inversely with x and y = 9 when x = 2. Write and equation for the inverse variation.

  12. a. xy 3 10 5 6 10 3 Check each product xy. 3(10) = 30     5(6) = 30     10(3) = 30 Decide if each data set represents a direct variation or aninverse variation. Then write an equation to model the data. Inverse? Inverse; xy = 30

  13. y x b. xy 2 3 4 6 8 12 Check each ratio . 12 8 6 4 = 1.5 3 2 = 1.5 = 1.5 Direct? Direct: y = 1.5x

  14. Homework Inverse Variation worksheet (“Practice 5-6”)

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