Algebra 1
Name:_________________________________
Homework #35: Direct Variation
Date:_________________ Block:___________
IDENTIFYING DIRECT VARIATION EQUATIONS: Tell whether the equation represents direct
variation. If so, identify the constant of variation.
1) y = x
__________
__________
2) y = 5x – 1
__________
__________
3) 2x + y = 3
__________
__________
4) x – 3y = 0
__________
__________
5) 2.4x + 6 = 1.2y __________
__________
6) Which equation is a direct variation equation?
A) y = 7 – 3x
B) 3x – 7y = 1
_______
C) 3x – 7y = 0
D) 3y = 7x – 1
7) ERROR ANALYSIS: Describe and correct the error in identifying the constant of variation
for the direct variation equation -5x + 3y = 0.
-5x + 3y = 0
3y = 5x
The constant of variation is 5.
Write the direct variation equation. Then find y when x = 8.
8) ____________ ___________
9) ____________ ____________
IDENTIFYING DIRECT VARIATION EQUATIONS: Tell whether the table represents direct
variation. If so, write the direct variation equation.
10) ____________ ___________
x
y
1
5
2
10
3
15
4
20
11) ____________ ___________
6
30
x
y
-3
-2
-1
0
1
2
3
4
5
6
WRITING EQUATIONS: Given that y varies directly with x, use the specified values to write a
direct variation equation that relates x and y.
12) x = 3, y = 9
____________
13) x = 14, y = 7
____________
14) x = 15, y = -5
____________
15) x = -6, y = 15
____________
16) The distance d (in meters) you travel on a bicycle varies directly with the number r of
revolutions that the rear tire completes. You travel about 2 meters on a mountain bijke for
every revolution of the tire.
a) Write a direct variation equation that relates r and d.
____________
b) How many meters do you travel in 1500 tire revolutions? ____________
17) At one company, the amount of vacation time v (in hours) varies directly with them amount
of time t (in weeks) he or she works. An employee who works 2 weeks earns 3 hours of
vacation.
a) Write a direct variation equation that relates t and v.
____________
b) How many hours of vacation time does an employee earn in 8 weeks? ____________
18) Landscapers plan to spread a layer of stone on a path. The number s of bags of stone
needed depends on the depth d (in inches) of the layer. They need 10 bags to spread a layer of
stone that is 2 inches deep.
a) Write a direct variation equation that relates d and s.
____________
b) How many bags of stone is needed to spread a layer that is 3 inches deep? ____________
19) At a recycling center, computers and computer accessories can be
recycled for a fee f based on the weight w, as shown in the table.
a) Write a direct variation equation that relates f and w.
___________
b) What is the total recycling fee for a computer that weighs
18 pounds and a printer that weighs 10 pounds.
_____________
Weight, w
(pounds)
Fee, f
(dollars)
10
15
30
2.50
3.75
7.50
20) You can buy gold chain by the inch. The table shows the price of gold chain for various
lengths.
Length, l
(inches)
Price, p (dollars)
7
9
16
18
8.75
11.25
20.00
22.50
a) Write a direct variation equation that relates l and p.
___________
b) If you have $30, what is the longest chain that you can buy? ___________
21) The weight, W, of a bass fish varies directly with its length, L. A 2-foot bass weighs 6
pounds. Write the equation that relates W and L.
A) W  6L
B) W  3L
C) L  3W
D) L  9W
22) Write the variation equation and find the quantity indicated: x varies directly with y.
If x is 54 when y is 100, find x when y is 200.
A) 1080
B) 27
C) 108
D) 370
10
27