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Understand direct, joint, inverse, and combined variation in mathematical equations through solved examples. Learn how to solve for k and find y or r based on given values of x and z. Practice problems included.

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  1. Splash Screen

  2. Concept

  3. Direct Variation If y varies directly as x and y = –15 when x = 5, find y when x = 3. Direct variation equation Use values that follow “if” Solve for k Example 1

  4. Direct Variation Substitute the value of k back into original equation find y when x = 3 Answer: When x = 3, the value of y is –9. Example 1

  5. A.–28 B. C. D. If y varies directly as x and y = 12 when x = –3, find y when x = 7. Example 1

  6. Concept

  7. Joint Variation Suppose y varies jointly as x and z. Find y when x = 10 and z = 5, if y = 12 when x = 3 and z = 8. Joint variation equation Use values that follow “if” Solve for k Example 2

  8. Joint Variation Substitute the value of k back into original equation Find y when x = 10 and z = 5 Answer: When x = 10 and z = 5, y = 25. Example 2

  9. A. B. C. D. Suppose y varies jointly as x and z. Find y when x = 3 and z = 2, if y = 11 when x = 5 and z = 22. Example 2

  10. Concept

  11. Inverse Variation If r varies inversely as t and r = –6 when t = 2, find r when t = –7. Inverse variation equation Use values that follow “if” Solve for k Example 3

  12. Inverse Variation Substitute the value of k back into original equation find r when t = –7 Answer: When t = –7, r is . Example 3

  13. A. B.4 C.16 D.144 If a varies inversely as b and a = 3 when b = 8, find a when b = 6. Example 3

  14. Combined Variation Suppose f varies directly as g, and f varies inversely as h. Find g when f = 6 and h = –5, if g = 18 when h = 3 and f = 5. Combined variation equation Use values that follow “if” Solve for k Example 5

  15. Combined Variation Substitute the value of k back into original equation Find g when f = 6 and h = –5 Answer: When f = 6 and h = –5, the value of g is –36. Example 5

  16. Suppose f varies directly as g, and f varies inversely as h. Find g when f = 6 and h = –16, if g = 10 when h = 4 and f = –6. A. –30 B. 30 C. 36 D. 40 Example 5

  17. Homework p. 566 # 3 – 45 (x3)

  18. End of the Lesson

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