What You Will Learn
• Recognize and solve direct and joint variation problems
• Recognize and solve inverse variation problems
Direct Variation• Can be expressed in the form y=kx
• K in this equation is called constant of variation
• Slope of a direct variation = constant of variation.
• As x increases, y increases or decreases at a constant rate (y varies directly as x)
• If you know [y varies directly as x] and one set of values, you can use a proportion to find the other set of corresponding values.
kx
y
kxy
1
1
11
2
2
1
1
x
y
x
y
kx
y
kxy
2
2
22
Joint Variation• When 1 quantity varies directly as
the product of two or more other quantities.
• Y varies jointly as x and z if there is some number k such that y=kxz
• If you know y varies jointly as x and z and one set of values, you can use a proportion to find the other set of corresponding values.
22
2
11
1
zx
y
zx
y
Suppose y varies jointly as x and z. Find y when x=8 and z=3, if y=16 when z=2 and x =5.
22
2
11
1
zx
y
zx
y
)3(8)2(5
16 2y
))(2(5)16)(3(8 2y
210384 y
24.38 y
Joint Variation
Cross Multiply
Divide by 10
Substitute numbers into the Joint Variation
Inverse Variation• As one quantity increases, the other
quantity decreases.
• If there is a nonzero constant k, xy=k or y=
x
k
Speed and time vary inversely with each other because when you travel somewhere, as your speed increases, the time it takes you to get there decreases.