Pre­Calc/Trig A
November 21, 2014
3­8 Direct, Inverse, and Joint Variation
3­8 Direct, Inverse, and Joint Variation
Pre­Calc/Trig A
November 21, 2014
A direct variation can be described by the equation y is related to a power of x by the constant of variation, k
Example: Suppose y varies directly as x and y=27 when x=6. Find the constant of variation.
3­8 Direct, Inverse, and Joint Variation
Pre­Calc/Trig A
November 21, 2014
Use the equation to find the value of y when x=10
3­8 Direct, Inverse, and Joint Variation
Pre­Calc/Trig A
November 21, 2014
Suppose y varies directly as x and y=96 when x=12, find the constant of variation. Use the equation to find y when x=5
3­8 Direct, Inverse, and Joint Variation
Pre­Calc/Trig A
November 21, 2014
Suppose y varies directly as the square of x and y=8 and x=4. Find the constant of variation. Use the equation to find x when y=50.
3­8 Direct, Inverse, and Joint Variation
Pre­Calc/Trig A
November 21, 2014
An inverse variation can be described by the equation Example: If y varies inversely as x and y=21 when x=15, find x when y=12
3­8 Direct, Inverse, and Joint Variation
Pre­Calc/Trig A
November 21, 2014
Example: If y varies inversely as the cube of x and y=3 when x=2, find the constant of variation. Use the equation to find the value of y when x=4.
3­8 Direct, Inverse, and Joint Variation
Pre­Calc/Trig A
November 21, 2014
A joint variation can be described by the equation Example: If y varies jointly as x and z and y=36 when x=1.2 and z=2, find y when x=0.4 and z=3
3­8 Direct, Inverse, and Joint Variation
Pre­Calc/Trig A
November 21, 2014
Example: If y varies jointly as x and the
cube of z and y=16 when x=4 and z=2,
find y when x=­8 and z=­3
3­8 Direct, Inverse, and Joint Variation
Pre­Calc/Trig A
November 21, 2014
Example: Suppose y varies jointly as x and z and inversely as w and y=­3 when x=2, z=­3, and w=4. Find y when x=4, z=­7, and w=­4.
3­8 Direct, Inverse, and Joint Variation