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9.5 = Variation Functions

9.5 = Variation Functions. Direct Variation. Direct Variation – y varies directly as x. Direct Variation – y varies directly as x y = k x. Direct Variation – y varies directly as x y = k x * Note: k = constant of variation (a #).

jacob-mccormick
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9.5 = Variation Functions

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  1. 9.5 = Variation Functions

  2. Direct Variation

  3. Direct Variation – y varies directly as x

  4. Direct Variation – y varies directly as x y = kx

  5. Direct Variation – y varies directly as x y = kx *Note: k = constant of variation (a #)

  6. Direct Variation – y varies directly as x y = kx *Note: k = constant of variation (a #) Inverse Variation

  7. Direct Variation – y varies directly as x y = kx *Note: k = constant of variation (a #) Inverse Variation – y varies inversely as x

  8. Direct Variation – y varies directly as x y = kx *Note: k = constant of variation (a #) Inverse Variation – y varies inversely as x y = k x

  9. Direct Variation – y varies directly as x y = kx *Note: k = constant of variation (a #) Inverse Variation – y varies inversely as x y = k x Joint Variation

  10. Direct Variation – y varies directly as x y = kx *Note: k = constant of variation (a #) Inverse Variation – y varies inversely as x y = k x Joint Variation – y varies jointly as x and z

  11. Direct Variation – y varies directly as x y = kx *Note: k = constant of variation (a #) Inverse Variation – y varies inversely as x y = k x Joint Variation – y varies jointly as x and z y = kxz

  12. Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation.

  13. Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20

  14. Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20

  15. Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20 b = 20 a

  16. Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20 b = 20 , inverse a

  17. Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20 b = 20 , inverse, k = 20 a

  18. Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20 b = 20 , inverse, k = 20 a b. y= -0.5 x

  19. Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20 b = 20 , inverse, k = 20 a b. y= -0.5 x y = -0.5x

  20. Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20 b = 20 , inverse, k = 20 a b. y= -0.5 x y = -0.5x , direct

  21. Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20 b = 20 , inverse, k = 20 a b. y= -0.5 x y = -0.5x , direct, k = -0.5

  22. Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20 b = 20 , inverse, k = 20 a b. y= -0.5 x y = -0.5x , direct, k = -0.5 c. A = ½bh

  23. Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20 b = 20 , inverse, k = 20 a b. y= -0.5 x y = -0.5x , direct, k = -0.5 c. A = ½bh , joint

  24. Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20 b = 20 , inverse, k = 20 a b. y= -0.5 x y = -0.5x , direct, k = -0.5 c. A = ½bh , joint , k = ½

  25. Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20.

  26. Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20.

  27. Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20. 1) y = kx

  28. Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20. 1) y = kx

  29. Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20. 1) y = kx 18 = k(15)

  30. Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20. 1) y = kx 18 = k(15) 18 = 15k

  31. Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20. 1) y = kx 18 = k(15) 18 = 15k 18= k 15

  32. Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20. 1) y = kx 18 = k(15) 18 = 15k 18= k 15 6= k 5

  33. Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20. 1) y = kx2) y = kx 18 = k(15) 18 = 15k 18= k 15 6= k 5

  34. Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20. 1) y = kx2) y = kx 18 = k(15)y = 6x 18 = 15k 5 18= k 15 6= k 5

  35. Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y whenx = 20. 1) y = kx2) y = kx 18 = k(15)y = 6x 18 = 15k 5 18= k 15 6= k 5

  36. Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y whenx = 20. 1) y = kx2) y = kx 18 = k(15)y = 6x 18 = 15k 5 18= k y = 6(20) 15 5 6= k 5

  37. Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y whenx = 20. 1) y = kx2) y = kx 18 = k(15)y = 6x 18 = 15k 5 18= k y = 6(20) 15 5 6= k y = 120 5 5

  38. Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y whenx = 20. 1) y = kx2) y = kx 18 = k(15)y = 6x 18 = 15k 5 18= k y = 6(20) 15 5 6= k y = 120 5 5 y = 24

  39. Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6

  40. 1) y = kxz Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6

  41. 1) y = kxz -90 = -6(15)k Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6

  42. 1) y = kxz -90 = -6(15)k -90 = -90k Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6

  43. 1) y = kxz -90 = -6(15)k -90 = -90k 1 = k Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6

  44. 1) y = kxz -90 = -6(15)k -90 = -90k 1 = k 2) y = kxz Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6

  45. 1) y = kxz -90 = -6(15)k -90 = -90k 1 = k 2) y = kxz y = 1xz Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6

  46. 1) y = kxz -90 = -6(15)k -90 = -90k 1 = k 2) y = kxz y = 1xz y = 1(9)(-5) Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6

  47. 1) y = kxz -90 = -6(15)k -90 = -90k 1 = k 2) y = kxz y = 1xz y = 1(9)(-5) y = -45 Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6 • If y varies inversely as x and y = -14 when x = 12, find x when y = 21

  48. 1) y = kxz -90 = -6(15)k -90 = -90k 1 = k 2) y = kxz y = 1xz y = 1(9)(-5) y = -45 Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6 • If y varies inversely as x and y = -14 when x = 12, find x when y = 21 1) y = k x -14 = k 12 -168 = k

  49. 1) y = kxz -90 = -6(15)k -90 = -90k 1 = k 2) y = kxz y = 1xz y = 1(9)(-5) y = -45 Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6 • If y varies inversely as x and y = -14 when x = 12, find x when y = 21 1) y = k x -14 = k 12 -168 = k 2) y = k x 21 = -168 x x = -8

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