1. Inverse, Joint, and Combined Variation
Objective: To find the constant of variation for many types of problems and to solve real world problems.

7. Inverse Variation
Two variables, x and y, have an inverse-variation relationship if there is a nonzero number k such that xy = k, y = k/x. The constant of variation is k.

8. Example 1

9. Example 1

10. Example 1

11. Try This
The variable y varies inversely as x, and y = 120 when x = Find the constant of variation and write an equation for the relationship. Then, find y when x is 1.5, 4.5, 8, 12.5, and 14.

12. Try This
The variable y varies inversely as x, and y = 120 when x = Find the constant of variation and write an equation for the relationship. Then, find y when x is 1.5, 4.5, 8, 12.5, and 14.

13. Try This
The variable y varies inversely as x, and y = 120 when x = Find the constant of variation and write an equation for the relationship. Then, find y when x is 1.5, 4.5, 8, 12.5, and 14.

14. Joint Variation
If y = kxz, then y varies jointly as x and z, and the constant of variation is k.

15. Example 2

16. Example 2

17. Squared Variation
If , where k is a nonzero constant, then y varies directly as the square of x. Many geometric relationships involve this type of variation, as show in the next example.

18. Example 3

19. Example 3

20. Example 3

21. Try This
Write the formula for the area A, of a circle whose radius is r. Identify the type of variation and the constant of variation.
Find the area of the circle when r is 1.5, 2.5, 3.5, 4.5.

22. Try This
Write the formula for the area A, of a circle whose radius is r. Identify the type of variation and the constant of variation.
Find the area of the circle when r is 1.5, 2.5, 3.5, 4.5.
The constant of variation is

23. Try This
Write the formula for the area A, of a circle whose radius is r. Identify the type of variation and the constant of variation.
Find the area of the circle when r is 1.5, 2.5, 3.5, 4.5.
The constant of variation is

24. Combined Variation

25. Example 4

26. Example 4

27. Example 4

29. Homework
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