Algebra I
Name:
SOL A.8 Direct/Inverse Variation
Block:
Date:
Direct/Inverse
Variation
Direct/Inverse Variation
Tell whether the equation represents direct variation, inverse variation or neither.
1) y = -4x
4)
y
=4
x
2) xy = 7
3) x = 7y
5) 3x + 4y = 8
6) 3x 
12
y
7) Given that y varies directly with x, and y = 15 when x = 12,
a) write a direct variation equation that relates x and y.
b) Find y when x = 8
8) Given that y varies inversely with x, and y = 15 when x = 12,
a) write an inverse variation equation that relates x and y.
b) Find y when x = 8
9) To travel a fixed distance, the rate varies inversely with the time required. When the rate is
60 miles per hour, the time required is 4 hours. What time would be required for the same
distance if the rate were increased to 80 miles per hour?
10) Do the tables below represents direct variation, inverse variation, or neither? If it represents
direct or inverse variation, find the constant of variation and write the equation.
a)
x
1 2 3
4
5
y
3 6 9 12 15
b)
x
1 2 3
4
5
y
2 4 9 16 25
c)
x
1
2
3 4 6
y
24 12 8 6 4
DV/IV/Neither: ____________
DV/IV/Neither: ____________
DV/IV/Neither: ____________
Constant of variation: _______
Constant of variation: _______
Constant of variation: _______
Equation: _________________
Equation: _________________
Equation: _________________
11) Given this set of ordered pairs:
{ (-4, 3), (-6, 2), (4, 16), (3, 12), (-2, -8), (3, 9), (4, 4), (-1, 12)}
a) Select three points that will create a direct variation relation.
b) Select three points that will create an inverse variation relation.
12) Point A is an element of a direct variation on the graph
to the right. Plot two points, other than A, that are also
elements of this direct variation.
13) The pressure P of a sample of gas at a constant temperature varies inversely as the volume V.
a) Use the data in the table to write a function that models this inverse
variation.
b) Use your equation to estimate the pressure when the volume is 6 in3.
Simplify the following expressions. Write your answers using exponents. Evaluate all
numbers with exponents of 5 or less.
14) (5 x) 2
15) (2ab)5
16)
17) ( y 5 )3
18) y 5 y 3
19) (x 3 y 5 )2
20) [(x  y)3 ]4
21) (3m7)4 · m3
22) (3x2 y)3 (4 x3 y5 )2