12.1: Inverse and Direct Variation
Name:__________________
Period:_________ Date:____
Direction Variation Equation: ______________________________
Inverse Variation Equation: ______________________________
Example 1: Do x and y show direct variation, inverse variation, or neither?
y
1.5
1. xy = 4.8
2. x 
________
________
y
x
5
3.
________
x
2
y
4. y = x + 2
5. 3y = 4x
6.
________
________
________
7. y 
2
x
________
Example 2: 1) The variables x and y vary directly, and y = 6 when x = 1.5.
a.
Write an equation that relates x and y. _____________
b. Find y when x 
4
. _______________
3
2) The variables x and y vary inversely, and y = 7.5 when x = 2.
a. Write an equation that relates x and y. _____________
b. Find y when
x  1.2 . _______________
3) The variables x and y vary inversely, and y = 2 when x = -6.
a. Write an equation that relates x and y. _____________
c.
Find y when
x  8 . _______________
Example 3: The volume of gas in a container varies inversely with the amount of pressure. A gas has volume
75 in
3
at a pressure of 25 lbs/in . Write a model relating volume and pressure.
2
________________________
If data points (x, y) show that xy is a constant, there is an inverse variation.
If data points (x, y) show that
y
is a constant, there is a direct variation.
x
1
Example 4: Do these data show inverse or direct variation, or none? If so, find a model.
a.
_________________
x
y
-5
-1.6
-2
-4
4
2
10
0.8
16
0.5
-1
0
1
2
3
4
5
6
2
10
3
15
4
20
6
30
9
11.25
16
20.00
18
22.50
4
2
8
2
16
6
-3
4
4
-3
8
-1.5
b. _________________
x
Y
c.
-3
-2
_________________
x
Y
1
5
d. _________________
x
y
e.
_________________
x
Y
f.
7
8.75
2
1
_________________
x
Y
-5
2.4
24
-0.5
Example 7: Write an equation.
1.
y varies directly with x
____________________
2.
y varies inversely with x.
____________________
3.
y varies inversely with the square of x.
____________________
4.
z varies directly with y and inversely with x.
____________________
2
5.
y varies directly with x and inversely with
z2 .
6.
y varies inversely with x .
____________________
7.
y varies directly with x and inversely with z.
____________________
8.
y varies inversely with x and z.
____________________
3
2
____________________
Example 8. The ideal gas law states that the volume V (in liters) varies directly with the number of
molecules n (in moles) and temperature T (in Kelvin) and varies inversely with the pressure P (in kilopascals).
The constant of variation is denoted by R and is called the universal gas constant.
a.
Write an equation for the ideal gas law. ____________________
b. Estimate the universal gas law constant if V=251.6 liters; n=1 mole; T=288 K; P=9.5
kilopascals.
____________________
Example 9: Graphs
Graph the inverse variation function y= y
Graph the equation y=2x.

2
x
y
y
x
x
HMK 4.6 B and 12.1 B graphing
3
3.8: Literal Equations
Quantity
Formula
Distance
d  rt
Temperature
F  C  32
Area of a triangle
9
5
1
A  bh
2
Solve
for the
variable
r
C
h
Area of a rectangle
A  lw
l
Perimeter of a
rectangle
Area of a trapezoid
P  2l  2w
W
Area of a circle
A  r 2
r
Circumference of a
circle
C  2r
r
A
1
h  b1  b2 
2
ANSWER
b1
WORK:
HMK 1.4 B A2 13-22 only
4