1. 1 Algebra 2: Section 9.1 Inverse and Joint Variation

2. 2 Direct Variation The variables x and y are in direct variation if… The variables x and y are in direct variation if… Inverse Variation The variables x and y are in inverse variation if… The variables x and y are in inverse variation if… k is the constant of variation k is the constant of variation As x gets bigger, y gets smaller (visa versa) As x gets bigger, y gets smaller (visa versa) k is the constant of variation k is the constant of variation As x gets bigger, y gets bigger As x gets bigger, y gets bigger

3. 3 The variables x and y vary inversely. Use the given values to write an equation of x and y.

4. 4 Joint Variation When one thing varies directly with two or more other quantities. When one thing varies directly with two or more other quantities. z varies jointly with x and y (varies jointly means they both vary directly)

5. 5 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=-4 and y=7.

6. 6 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=3 and y=-2.

7. Direct Variation Direct Variation Inverse Variation Inverse Variation Joint Variation Joint Variation None None EX: Identify each equation as a direct variation, inverse variation, joint variation or none. (may need to solve for y)

8. 8 Write an equation for the given relationship. 5. y varies directly with x and inversely with z 2 Notice…… Notice…… Any variable that varies directly is in the numerator Any variable that varies directly is in the numerator Any variable that varies indirectly is in the denominator Any variable that varies indirectly is in the denominator

9. 9 6. x varies inversely with the square of y 7. z varies jointly with x and y and inversely with the square root of a

10. Determine if each is a direct variation, inverse variation, or neither? Determine if each is a direct variation, inverse variation, or neither? Divide x/y and look at ratios….. Divide x/y and look at ratios….. Inverse Variation: As x gets bigger, y gets smaller. Inverse Variation: As x gets bigger, y gets smaller. Direct Variation: As x gets bigger, y gets bigger. Direct Variation: As x gets bigger, y gets bigger. XY 1002 504 258 8 x23.54.2 y4.57.8759.45

11. 11 Homework p.537 #21 – 24 all p.537 #21 – 24 all #29 – 47 all

12. WORD PROBLEMS??? 12