Algebra – Unit 4 - Slope
HOMEWORK # 4 – Inverse Variation
Inverse Variation Practice
1) Do the tables below represent direct variation, inverse variation, or neither? If it
represents a direct or inverse variation, find the constant of variation, and write an
equation for the function.
a)
b)
c)
x 0.5 2
6
x 0.2 0.6 1.2
x
1
2
3
y 1.5 6
18
y
12
4
2
y
2
1
1.5
Direct/Inverse
Variation/Neither? ________
Constant of Variation:_______
Equation: _______________
Direct/Inverse
Variation/Neither? ________
Constant of
Variation:_______
Equation: _______________
Direct/Inverse
Variation/Neither? ________
Constant of Variation:_______
Equation: _______________
d)
e)
f)
x
y
0.8
0.9
0.6
1.2
0.4
1.8
Direct/Inverse
Variation/Neither? ________
Constant of Variation:_______
Equation: _______________
x
y
2
3.2
4
1.6
6
1.1
Direct/Inverse
Variation/Neither? ________
Constant of
Variation:_______
Equation: _______________
x
y
1.2
18
1.4
21
1.6
24
Direct/Inverse
Variation/Neither? ________
Constant of Variation:_______
Equation: _______________
2) Suppose that x and y vary inversely. Write a function that models the each inverse
variation, and find y when x = 10.
a) x = 20 when y = 5
b) x = 20 when y = -4
Function: _______
Function: _______
When x = 10, y = ________
When x = 10, y = ________
c) x = 5 when y = -
1
3
Function: _______
When x = 10, y = ________
3) Each ordered pair is from an inverse variation. Find the constant of variation, and write
the function.
a) (6, 3)
b) (0.9, 4)
3 2
c)  , 
8 3
Constant of Variation:_______ Constant of
Constant of Variation:_______
Variation:_______
Function: _______________
Function: _______________
Function: _______________
4) Each pair of values is from an inverse variation. Find the missing values.
a) (2, 6), (4, y)
b) (4, 6), (x, 3)
c) (9,5), (x, 3)
5) The speed of a laundry truck varies inversely with the time it takes to reach its
destination. If the truck takes 3 hours to reach its destination traveling at a constant
speed of 50 miles per hour, how long will it take to reach the same location when it
travels at a constant speed of 60 miles per hour?
6) 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.
7) Bob's dentist determined the number of cavities developed in his patient's mouth each
year is inversely proportional to the total number of minutes spent brushing during each
session. If Bob developed four cavities during the year he spent only 30 seconds
brushing his teeth each time, how many annual cavities will Bob develop if he increases
his brushing time to two minutes per session?
8) A recipe for 2 dozen corn muffins calls for 3 cups of flour. The number of muffins varies
directly with the amount of flour you use. How many cups of flour are needed to make 6
dozen muffins?
9) The number of workers on a job varies inversely to the time needed to finish a project. If
4 workers can complete a brick patio in 20 hours, how many workers are needed to
finish the job in 5 hours?
10) The efficiency department of a mail and phone order company discovered the accuracy
of phone orders varied inversely to the number of hours in the operator’s shift. If
employees who worked 2 hour shifts were 98% accurate, how many hours were worked
by those with 24.5% accuracy?
11) Kelly’s coach believes every player should have an equal opportunity to play. As a
result Kelly’s playing time is inversely proportional to the number of players who show
up for a game. When the whole team of 16 players attends, each player has 18 minutes
of playing time. How many players must be absent for Kelly to play 24 minutes?