# 5.1 Direct and Inverse Variation

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```Algebra 2/Trigonometry 1
Name: ____________________________
Direct and Inverse Variation
Notes Sheet
Two variables, x and y, display direct variation if and only if y  kx for some constant k.
Two variables, x and y, display inverse variation if and only if y  kx for some constant k.
k is called the constant of variation.
Example: Determine whether the following equations display direct variation, inverse
variation, or neither.
y
x  10y
y  8x
4y  x
xy  2
y  2x  1
y  3x
2  x
DV
IV
DV
IV
DV
N
IV
Example: Write an equation for the given relationship.
a) y varies directly with the square of x.
b) z varies jointly with x and y.
c) z varies directly with y and inversely with x.
Solution: y  kx2
Solution: y  kxy
Solution: y  kyx
Example: Follow the given type of variation and use the given values to write an equation
relating x and y. Use this equation to find y when x = 5.
Inverse Variation: x  3 , y  6
Direct Variation: x  4 , y  8
Example: The law of universal gravitation states that the gravitational force F (in
newtons) between two objects varies jointly with their masses m1 and m2 (in kilograms)
and inversely with the square of the distance d (in meters) between the two objects. The
constant of variation is denoted by G and is called the universal gravitational constant.
Gm1 m2
a) Write an equation for the law of universal gravitation.
Solution: F 
d2
b) Estimate the universal gravitational constant using the following facts about the
Earth and Sun.
Mass of Earth: m1  5.98  10 24 kg
Mass of Sun: m2  1.99  1030 kg
Mean Distance Between Earth and Sun: d  1.50  1011 m
Force Between Earth and Sun:: F  3.53  10 22
Solution: 6.67  10 11
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