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Immediate and Inverse Variations

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  1. Direct and InverseVariations section 9-2

  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. Direct Variation • the gist of direct variation is the following formula:

  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. Direct Variation • if y varies directly as x and y = 10 as x = 2.4, 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. Direct Variation • if y varies directly as x and y = 10 as x = 2.4, find x when y =15

  7. Direct Variation • How do we solve this? Cross multiply and set equal.

  8. Direct Variation • We get: 10x = 36 • Solve for x by diving both sides by 10. • We get x = 3.6

  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. Direct Variation • If y varies directly with x and y = 12 when x = 2, find y when x = 8.

  11. Direct Variation • Cross multiply: 96 = 2y • Solve for y. • 48 = y.

  12. Direct Variation • From the 9-2 Study Guide, complete problems 2, 4, & 7.

  13. Direct Variation • #2 • 6y = 72 • y = 12

  14. Direct Variation • #4 • 135 = 5x • x = 27

  15. Direct Variation • #7 • 200,000 = 50x • x = 4000

  16. 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.

  17. Inverse Variation • With Direct variation we Divide our x’s and y’s. • In Inverse variation we will Multiply them. • x1y1 = x2y2

  18. 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

  19. 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

  20. Inverse Variation • Try some on your own. • On your worksheet: • # 1, 6, 8

  21. Inverse Variation • #1 • 15(y) = 10(12) • 15y = 120 • y = 8

  22. Inverse Variation • #6 • 27(x) = 9(45) • 27x = 405 • x = 15

  23. Inverse Variation • #8 • 76(y) = 38(100) • 76y = 3800 • y = 50

  24. Direct & Inverse Variation • Assignment - wkst 9-2 • 1-8