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1. Direct Inverse joint

2. VARIATION

3. The general equation for DIRECT VARIATION is k is called the constant of variation. We will do an example together.

4. If y varies directly as x, and y=24 and x=3 find: (a) the constant of variation (b) Find y when x=2 (a) Find the constant of variation Write the general equation Substitute

5. (b) Find y when x=2 First we find the constant of variation, which was k=8 Now we substitute into y=kx.

6. Another method of solving direct variation problems is to use proportions. Therefore...

7. So lets look at a problem that can by solved by either of these two methods.

8. If y varies directly as x and y=6 when x=5, then find y when x=15. Proportion Method:

9. Now lets solve using the equation. Either method gives the correct answer, choose the easiest for you.

10. Now you do one on your own. y varies directly as x, and x=8 when y=9. Find y when x=12. Answer: 13.5

11. What does the graph y=kx look like? A straight line with a y-intercept of 0.

12. y varies inversely as x if such that xy=k or Just as with direct variation, a proportion can be set up solve problems of indirect variation. Inverse Variation

13. A general form of the proportion Lets do an example that can be solved by using the equation and the proportion.

14. Find y when x=15, if y varies inversely as x and x=10 when y=12 Solve by equation:

15. Solve by proportion:

16. Solve this problem using either method. Find x when y=27, if y varies inversely as x and x=9 when y=45. Answer: 15

17. Joint Variation For three quantities x, y and z, if there is a constant k such that z = kxy We say “z varies jointly as y and x” or “z is jointly proportional to x and y”.

18. A general form of the proportion Lets do an example that can be solved by using the equation and the proportion.

19. Example 9 • U varies jointly as V and the square of W. if V =4 and W = 3, then U = 18. Find the value of V when U = 24 and W = 3.

20. Class work… • Work book page 123 and 124 even