Name:________________________________
Date:________
Period:___________
MPJH
Notes and Homework - Direct Variation
Equation y = kx
Table
x
(k≠ 0 k
3
6
9
constant of variation)
12
15
y
15
30
45
60
75
𝒚
𝒙
5
5
5
5
5
Graph
𝒚
𝒙
=𝒌
constant of variation
Is a line through the
origin (0,0)
With constant of variation
“k” as the slope
𝒚 = 𝒌𝒙
If x increases, y____________
If x decreases, y ___________
I.
Tell whether the equation represents a direct variation. Circle your answer. If it
represents a direct variation, find “k” the constant of variation.
4
1. 𝑦 = 𝑥
Yes
No
Constant of variation ___________________
2. 3𝑥 + 4𝑦 = 0
Yes
No
Constant of variation ___________________
3. 𝑦 = 5𝑥 − 3
Yes
No
Constant of variation ___________________
4. 𝑥𝑦 = 12
Yes
No
Constant of variation ___________________
3
II.
Tell whether the table represents a direct variation. Circle your answer. If it
represents a direct variation, find “k” the constant of variation.
1.
Yes
x
3
6
9
12
15
y
15
30
45
60
75
x
-3
-1
1
3
5
y
-2
0
2
4
6
No
Constant of variation _____________
2.
Yes
3.
Yes
Constant
Length 7
9
16
l (in.)
Price
8.75 11.25 20
P($)
18
No
Constant of variation _____________
20
22.5 25
No
of variation ____________
III.
Given that y varies directly with x, use the specified values to write a direct
variation equation that relates x and y.
1. 𝑥 = 2, 𝑦 = 26
________________________
2. 𝑥 = −5.2, 𝑦 = 1.4
________________________
3. 𝑥 = −6, 𝑦 = 15
________________________
4. 𝑥 = −2, 𝑦 = −2
________________________
IV.
At one company the amount of vacation v (in hours) an employee earns varies directly with the
amount of time t (in weeks) he or she works. An employee who works for 2 weeks earns 3 hours
of vacation.
Write a direct variation equation that relates t and v. _________________________
V.
At a recycling center computers can be recycled for a fee f based on weight w.
f varies directly with w. A computer that weighs 10 pounds is charged a fee of $2.50.
Write a direct variation equation that relates f and w. _________________________
VI.
The distance d (in meters) you travel on a bike varies directly with the number of revolutions r
that the rear tire completes. You travel 4 meters on a mountain bike for every 2 revolutions.
Write a direct variation equation that relates r and d. _________________________
VII.
The cost C (in $) of downloading songs varies directly with the number of songs s from an
internet music website. The cost for downloading 3 songs is $2.97.
Write a direct variation equation that relates C and s. ________________________