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 = kx ) 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 = kx ) y = kx
18 = k(15) y = 6x
18 = 15k
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 when x = 20.
1) y = kx ) y = kx
18 = k(15) y = 6x
18 = 15k
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 when x = 20.
1) y = kx ) y = kx
18 = k(15) y = 6x
18 = 15k
18 = k y = 6(20)
6 = k 5

37. 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 ) y = kx
18 = k(15) y = 6x
18 = 15k
18 = k y = 6(20)
6 = k y = 120

38. 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 ) y = kx
18 = k(15) y = 6x
18 = 15k
18 = k y = 6(20)
6 = k y = 120
y = 24

39. Suppose y varies jointly as x and z
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. Suppose y varies jointly as x and z
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
1) y = kxz

41. Suppose y varies jointly as x and z
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
1) y = kxz
-90 = -6(15)k

42. Suppose y varies jointly as x and z
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
1) y = kxz
-90 = -6(15)k
-90 = -90k

43. Suppose y varies jointly as x and z
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
1) y = kxz
-90 = -6(15)k
-90 = -90k
1 = k

44. Suppose y varies jointly as x and z
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
1) y = kxz
-90 = -6(15)k
-90 = -90k
1 = k
2) y = kxz

45. Suppose y varies jointly as x and z
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
1) y = kxz
-90 = -6(15)k
-90 = -90k
1 = k
2) y = kxz
y = 1xz

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

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

48. If y varies inversely as x and y = -14 when x = 12, find x when y = 21
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
1) y = kxz
-90 = -6(15)k
-90 = -90k
1 = k
2) y = kxz
y = 1xz
y = 1(9)(-5)
y = -45
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. If y varies inversely as x and y = -14 when x = 12, find x when y = 21
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
1) y = kxz
-90 = -6(15)k
-90 = -90k
1 = k
2) y = kxz
y = 1xz
y = 1(9)(-5)
y = -45
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 = -8