2. Direct and Inverse Variations

3. 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.

4. Direct Variation Direct variation uses the following formula:

5. 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?

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. We will apply what we know and try this problem. According to Hook’s Law, the force F required to stretch a spring x units beyond its natural length varies directly as x. A force of 30 pounds stretches a certain spring 5 inches. Find how far the spring is stretched by a 50 pound weight.

13. Set up a proportion Substitute

15. 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.

16. Inverse Variation With Direct variation we Divide our x’s and y’s. In Inverse variation we will Multiply them. x 1 y 1 = x 2 y 2

17. Inverse Variation If y varies inversely with x and y = 12 when x = 2, find y when x = 8. x 1 y 1 = x 2 y 2 2(12) = 8y 24 = 8y y = 3

18. 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

19. Lets apply what we have learned. The pressure P of a compressed gas is inversely proportional to its volume V according to Boyle’s Law. A pressure of 40 pounds per square inch is created by 600 cubic inches of a certain gas. Find the pressure when the gas is compressed to 200 cubic inches.

20. Step #1: Set up a proportion.