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Honors Algebra 1
Unit 4 – Linear Functions
Name: ______________________
Honors Homework – Direct and Inverse Variation
DEFINITIONS
Direct Variation – a linear relationship between x and y, where x and y maintain a constant
ratio/quotient. (These are the relationships explored in lessons 1 and 3 from unit 4)
y
 Identified as y  kx or  k
x
Inverse Variation – a non-linear relationship between x and y, where x and y maintain a constant
product
k
 Identified as y  or y  x  k
x
For both direct and inverse variation, the constant quotient/product (k) is called the constant of variation
Table A
Table B
x
y
x
y
1
4
3
20
2
8
6
10
3
12
12
5
Examples
y
 4 every time. Table A is an
x
example of direct variation (k = 4). The equation for Table A would therefore be y  f  x   4 x

For table A, y  x is different for every row (4, 16, and 36), but

For table B,
y
is different for every row (none of them whole numbers), but y  x  60 every time.
x
Table B is an example of inverse variation (k = 60). The equation for Table B would therefore be
60
y  f  x 
x
Homework Questions – Complete the following exercises using the methods above
A) Identify the tables as direct or inverse variation (if it’s either of them!) and give the constant of
variation.
1)
x
10
15
20
y
2
3
4
x
2)
y
1
2
-30 -15
3
-10
3)
x
2
8
4
y
12
3
6
Direct/Inverse
Direct/Inverse
Direct/Inverse
k = ________
k = ________
k = ________
OVER
B) Answer the following questions.
1) If y varies inversely as x and x = 5 when
y = 4, find y when x = 2.
2) If y varies directly as x and y = 9 when x = 2,
find x when y = 22.5.
3) The variable x varies directly with y. When x
is 10, y is 70. Find y when x is 14.
4) In a formula, Z varies inversely as p. If Z is
200 when p = 4, find Z when p = 10.
5) The amount of time to paint a house varies
inversely with the number of people painting.
If it takes 4 hours for 6 people to paint a
house, how many people would be needed to
do it in 3 hours?
6) The distance traveled in a car driving at a
constant speed varies directly with the time
driven. If it takes 3 hours to drive 168 miles,
how long will it take to drive 238 miles?