CP Algebra II 4/5/16 8.5 Variation Name:______________________________________ Direct variation is expressed in the form ! y = kx , where k is the constant of variation. EX #1: If y varies directly with x and! y = 8 when!x = 2 , find y when !x = 6 . Joint variation occurs when on quantity varies directly as the product of two or more other quantities. EX #2: Suppose y varies jointly as x and z. If ! y = 60 when !z = 4 and!x = 3 , find ! y when !x = 6 and !z = 8 If two quantities x and y show inverse variation, their product is equal to a constant k. k
That is, !xy = k , or y = . x
!
x
EX #3: If y varies inversely as x and ! y = 16 when! = 4 , find y when !x = 3 Combined variation occurs when one quantity varies directly and/or inversely as two or more other quantities. EX #4: Suppose y varies directly as x , and y varies inversely as z. Find z when x = 2 and y = 37.5, if x = 12.5 when z = 5 and y = 10. Practice: State whether each equation represents a direct, joint, inverse, or combined variation. Then name the constant of variation. 1. !C = 2π r 4
2. p = ! q
1
3. A = bh 2
!
4. !rw = 15 5. ! y = 2rgt 6. If y varies directly as x and ! y = 35 when !x = 7 , find y when x = 11. 7. If y varies jointly as x and z and y = 18 when x = 2 and z = 3, find y when x is 5 and z is 6. 8. If y varies inversely as x and y = 2 when x = 2, find y when x = 1. 9. If y varies directly as z and inversely as x and y = 27 and z = -­‐3 when x = 2, find x when y = 9 and z = 5. 10. If y varies directly as z and inversely as x and y = -­‐15 and z = 5 when x = 5, find x when y = -­‐36 and z = -­‐3.