1. 9.1 Inverse & Joint Variation By: L. Keali’i Alicea

2. Just a reminder from chapter 2 Direct Variation Use y=kx. Means “y v vv varies directly with x.” k is called the c cc constant of variation.

3. New stuff! Inverse Variation varies inversely “y varies inversely with x.” constant of variation k is the constant of variation.

4. Ex: tell whether x & y show direct variation, inverse variation, or neither. a.xy=5 b.x+y = 7 c. Hint: Solve the equation for y and take notice of the relationship. Inverse Variation Neither Direct Variation

5. Ex: The variables x & y vary inversely. Use the given values to write an equation relating x and y. Then find y when x =4. x=2, y=4 k=8 Find y when x= 4. y= 2

6. Ex: The variables x & y vary inversely. Use the given values to write an equation relating x and y. Then find y when x =4. x=16, y= 1/4 k=(1/4)16= 4 Find y when x= 4. y= 1

7. Joint Variation When a quantity varies directly as the product of 2 or more other quantities. For example: if z varies jointly with x & y, then z=kxy. Ex: if y varies inversely with the square of x, then y=k/x 2. Ex: if z varies directly with y and inversely with x, then z=ky/x.

8. Examples: Write an equation. y varies directly with x and inversely with z 2. y varies inversely with x 3. y varies directly with x 2 and inversely with z. z varies jointly with x 2 and y. y varies inversely with x and z.

9. 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= 4. x= 1, y=2, z=6 We use: z = kxy We put in the values for z, x, and y to solve for k. 6= k(1)(2) Then solve for k. k= 6/2 = 3 z = 3xy We then put in the values for x and y and solve for z. z= 3(-3)(4)= -36

10. Assignment 9.1 B (2-12 even, 13- 18)