7.1 Inverse & Joint Variation

1. Book – Unit 8.1 (page 551) 7.1Inverse & Joint Variation

2. Review • DIRECT VARIATION Direct variation is in the form y = ax where a is the constant of variation. • EX: Are the following direct variation? y = 3x y = -½x y = 5x – 1 YES YES NO y-intercept must be 0 for direct variation

3. Inverse Variation Joint Variation is when more than one variable are multiplying with a constant of variation. (it is more like direct variation for the set-up) EX: r = kgh

4. Example 1 • Tell whether x and y show direct variation, inverse variation, or neither (rewrite if needed) xy = 7 y = x + 3 Inverse Neither Direct

5. Example 2 • x & y vary inversely, and y = 7 when x = 4. Write an equation that relates x and y. Then, find y when x = -2 • Write the general equation • Substitute 7 for y and 4 for x • Solve for a. • Plug a into the general equation.

6. Example 2 Plug in -2 for x Solve for y

7. Example 3 • The number of songs that can be stored on an MP3 player varies inversely with the average size of a song. A certain MP3 player can store 2500 songs when the average size of a song is 4 MB. • Write a model that gives the number of songs, n, that will fit on the MP3 player as a function of the average song size s.

8. Example 3 Write the general equation Substitute 2500 for yand 4 for x Solve for a. Write the equation

9. On your own • Tell whether x and y show direct variation, inverse variation, or neither • a. 3x = y • b. xy = 0.75 • c. y = x – 5 Direct Variation Inverse Variation Neither

10. On your own • The variables x and y vary inversely. Use the given values to write an equation relating x and y. Then find y when x = 2. • a. x = 4, y = 3 • b. x = 8, y = -1 • c. x = ½, y = 12 y = 6 y = -4 y = 3

11. On your own • The area A of a computer chip is 58 mm2, and the number c of chips that can be obtain from a silicon wafer is 448. Write the model of this situation if A and c vary inversely. Then, find out how many chips will fit on a silicon wafer, if the area of the chip is 66 mm2.

12. Joint Variation • Joint variation occurs when a quantity varies directly with the product of two or more other quantities. In the equation, a is a nonzero constant. z varies jointly with x and y p varies jointly with q, r, and s

13. Example 4 • The variable z varies jointly with x and y. Also, z = -75 when x = 3 and y = -5. Write an equation that relates x, y, and z. Then find z when x = 2 and y = 6. • Write the general equation • Substitute in for x, y, and z • Solve for a.

14. Example 4 Rewrite the equation plugging in the value of a Calculate what z is when x = 2 and y = 6

15. Example 5 Write an equation for the given relationship a. y varies inversely with x b. z varies jointly with x, y, and r c. y varies inversely with the square of x d. z varies directly with y and inversely with x e. x varies jointly with t and r and inversely with s

16. On your own The variable z varies jointly with x and y. Use the given values to write an equation relating x, y, and z. Then find z when x = -2 and y = 5. a. x = 1, y = 2, z = 7 b. x = 4, y = -3, z = 24 c. x = -2, y = 6, z = 18

17. On your own Write an equation for the given relationships a. x varies inversely with y and directly with w b. p varies jointly with q and r and inversely with s

19. Homework Page 555 # 3 – 9 odd, 13-19 odd, # 25 & 27 HOMEWORK CHECK NEXT CLASS!!!!