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Algebra II

9-1 Notes. Algebra II. Direct Variation. Direct Variation: Two variables, y and x, vary directly if: y = If k is any nonzero constant. Example: The equation: y = 5x exhibits direct variation because:. Inverse Variation.

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Algebra II

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  1. 9-1 Notes Algebra II

  2. Direct Variation Direct Variation: Two variables, y and x, vary directly if: y = If k is any nonzero constant. Example: The equation: y = 5x exhibits direct variation because:

  3. Inverse Variation • Inverse Variation: Two variables, x and y, vary inversely if: y = for any nonzero constant, k Example: y = 5/x exhibits inverse variation because:

  4. Joint Variation • Joint Variation: Three variables, x, y, and z vary jointly if: z = for any non-zero constant, k. Example: z = 5xy exhibits joint variation because:

  5. Example 1: Determine if the following exhibit direct or inverse variation: a. xy = 10 b. y = x – 1 c. x = 5y

  6. OYO • Determine if the following equations exhibit direct variation, inverse variation, or neither: • 2y = x – 1 • 5y = 2x

  7. Example 2: • The variables x and y vary inversely, and y – 8 when x = 3. • a. Write an equation that relates x and y: • b. Use your equation from part a. to find y when x = -4

  8. Example 3: • Determine whether x and y show direct variation, inverse variation, or neither in the following tables:

  9. Example 4: • The variable z varies jointly with x and y. Use the given values to write and equation relating x, y, and z: x = 1, y = 1/3, and z = 5

  10. OYO • The variable z varies jointly with x and y. Use the given values to write and equation relating x, y, and z: • x = 5/6, y = 3/10, and z = 8

  11. Example 5: Write an equation for the given relationship: X varies inverssely with y and directly with z:

  12. OYO Write an equation for the given relationship: m varies inversely with a and jointly with b and c:

  13. Homework • Section 9-1: Page 537, # 22-46 even, and 54

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