Direct and Inverse variations

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Direct and Inverse variations

  1. 1. Direct and Inverse Variations
  2. 2. Direct Variation When we talk about a direct variation, we are talking about a relationship where as x increases, y increases or decreases at a CONSTANT RATE.
  3. 3. Direct Variation y1 x1 = y2 x2 Direct variation uses the following formula:
  4. 4. Direct Variation example: if y varies directly as x and y = 10 as x = 2.4, find x when y =15. what x and y go together?
  5. 5. Direct Variation If y varies directly as x and y = 10 find x when y =15. y = 10, x = 2.4 make these y1 and x1 y = 15, and x = ? make these y2 and x2
  6. 6. Direct Variation if y varies directly as x and y = 10 as x = 2.4, find x when y =15 10 2.4 = 15 x
  7. 7. Direct Variation How do we solve this? Cross multiply and set equal. 10 2.4 = 15 x
  8. 8. Direct Variation We get: 10x = 36 Solve for x by diving both sides by 10. We get x = 3.6
  9. 9. Direct Variation Let’s do another. If y varies directly with x and y = 12 when x = 2, find y when x = 8. Set up your equation.
  10. 10. Direct Variation If y varies directly with x and y = 12 when x = 2, find y when x = 8. 12 2 = y 8
  11. 11. Direct Variation Cross multiply: 96 = 2y Solve for y. 48 = y. 12 2 = y 8
  12. 12. Inverse Variation Inverse is very similar to direct, but in an inverse relationship as one value goes up, the other goes down. There is not necessarily a constant rate.
  13. 13. Inverse Variation With Direct variation we Divide our x’s and y’s. In Inverse variation we will Multiply them. x1y1 = x2y2
  14. 14. Inverse Variation If y varies inversely with x and y = 12 when x = 2, find y when x = 8. x1y1 = x2y2 2(12) = 8y 24 = 8y y = 3
  15. 15. Inverse Variation If y varies inversely as x and x = 18 when y = 6, find y when x = 8. 18(6) = 8y 108 = 8y y = 13.5

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