Download TOPIC # 5 – 6: Direct and Inverse Variation

Unit 8: Day 1
Direct and Inverse Variation
Definition…

Direct Variation: y varies directly as x
This means as x increases, y __________
increases!
decreases!
as x decreases, y __________
x
Hrs worked
5
11
14
17
y
pay
30.00
66.00
84.00
102.00
How would you find the constant rate?
Divide the pay by the hours worked!
The constant is $6 per hour!
The more hours you work, the more you earn!
General Equation for direct variation:
y
 constant
x
1. If y varies directly as x and y = 6
when x = 8, find y when x = 12.
Use the general equation
for direct variation, set up
a proportion and solve!
6 y

8 12
Cross-multiply!
8 y  72
Solve for y
(divide both
sides by 8)
y
 constant
x
y=9
2. The force required to stretch a spring, F, varies
directly with the amount the spring is stretched, s.
Ten pounds is needed to stretch a spring 8 inches.
How many pounds would be needed to stretch the
spring 32 inches?
Use the general equation
for direct variation, set up
a proportion and solve!
10 F

8 32
Cross-multiply!
8F  320
Solve for F
(divide both
sides by 8)
F
 constant
s
F = 40 lbs
3. The distance, d, varies directly with the
time, t. If you have driven 175 miles for 5
hours. How long would you drive for
210 miles?
Use the general equation
for direct variation, set up
a proportion and solve!
175 210 175t  1050

5
t Solve for t
Cross-multiply!
(divide both
sides by 175)
d
 constant
t
t = 6 hrs
Definition…

Inverse Variation: y varies inversely as x
This means as x increases, y __________
decreases!
increases!
as x decreases, y __________
x
Miles
18
20
30
60
y
Gal of gas
10
9
6
3
How would you find the constant rate?
Multiply miles and gallons!
The constant is 180 miles!
The more you drive, the less gas you have!
General Equation for inverse variation:
x  y  constant
4. If y varies inversely as x and y = 6
when x = 2, find x when y = 4.
Use the general equation
for inverse variation, set
up an equation and solve!
x  y  constant
(2)(6)  ( x)( 4)
12  4x
Solve for x (divide both sides by 4)
x=3
5. The volume, V, of a gas at constant temperature
varies inversely with the pressure, P. When the
volume is 100 cubic inches, the pressure is 25
pounds. Find the volume when the pressure is 50
pounds.
Use the general equation
for inverse variation, set
up an equation and solve!
VP  constant
(100)( 25)  (V )(50)
2500  50V
Solve for V (divide both sides by 50)
V = 50 in3
6. The number of slices, n, cut from a bread loaf of
constant length varies inversely as the uniform
thickness, t, of each slice. When there are 16
slices, each slice is 15mm thick. Find the number
of slices when the thickness is 12mm.
Use the general equation
for inverse variation, set
up an equation and solve!
(16)(15)  (n)(12)
240  12n
nt  constant
n = 20 slices
Solve for n (divide both sides by 12)