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WorksheetsDirect and Inverse Variation
Total questions: 100
Worksheet time: 4hrs 35mins
Name
Class
Date
1.
a)
direct variation
b)
inverse variation
c)
neither direct nor inverse variation
2.
a)
direct variation
b)
inverse variation
c)
neither direct nor inverse variation
3.
The equation
xy = 25 represents:
xy = 25 represents:
a)
direct variation
b)
inverse variation
c)
joint variation
d)
none of these
4.
a)
direct variation
b)
inverse variation
c)
joint variation
d)
none of these
5.
a)
direct variation
b)
inverse variation
c)
joint variation
d)
none of these
6.
a)
direct variation
b)
inverse variation
c)
joint variation
d)
none of these
7.
Suppose y varies directly as x.
If y = 22.5 when x = 15, find y when x = 20.
If y = 22.5 when x = 15, find y when x = 20.
a)
1.5
b)
337.5
c)
30
d)
16.875
8.
Suppose y varies inversely with x.
If y = 150 when x = 2, find y when x = 25.
If y = 150 when x = 2, find y when x = 25.
a)
300
b)
75
c)
1,875
d)
12
9.
Which of the following represents direct variation?
a)
y = kx
b)
y = k/x
c)
y = x/k
d)
y = mx + b
10.
Which of the following represents indirect variation?
a)
y = kx
b)
y = k/x
c)
y = x/k
d)
y = mx + b
11.
Y varies directly with x, and y is 84 when x is 16. Which equation represents this situation?
a)
y=1344x
b)
y=100x
c)
y=5.25x
d)
y=4/21x
12.
The width of a rectangle varies inversely with its length. If the width is 6 when the length is 24, give an equation that shows the relationship.
a)
y = 4x
b)
y = 144x
c)
y = 4/x
d)
y = 144/x
13.
The Height of a wave in California varies directly with the seconds that pass by. At 4 seconds, the wave is 6 feet high. How many seconds will give you a wave that is 10 feet high?
a)
y = 2/3x
b)
6
c)
6.6
d)
7
14.
The number of kilograms of water in a person’s body varies directly as the person’s mass. A person with a mass of 90 kg contains 60 kg of water. How many kilograms of water are in a person whose mass is 75 kg?
a)
50 kg water
b)
72 kg water
c)
94 kg water
d)
150 kg water
15.
The interest received on a savings account varies directly with the amount deposited. Daniel received $55.35 in interest on $1230 he deposited. How much interest would Daniel have received if he had deposited $2000 into his account?
a)
34.04
b)
90.00
c)
1,285.35
d)
44,444.44
16.
a)
direct variation
b)
inverse variation
c)
neither direct nor inverse variation
17.
a)
direct variation
b)
inverse variation
c)
neither direct nor inverse variation
18.
Which of the following represents direct variation?
a)
y = kx
b)
y = k/x
c)
y = x/k
d)
y = mx + b
19.
Y varies directly with x, and y is 84 when x is 16. Which equation represents this situation?
a)
y=1344x
b)
y=100x
c)
y=5.25x
d)
y=4/21x
20.
If y = 15 when x = 12 find y when x = 32.
a)
40
b)
-40
c)
5
d)
-5
21.
The width of a rectangle varies inversely with its length. If the width is 6 when the length is 24, give an equation that shows the relationship.
a)
y = 4x
b)
y = 144x
c)
y = 4/x
d)
y = 144/x
22.
A person’s weekly pay is directly proportional to the number of hours worked. Shawn’s pay is $123.00 for 20 hours of work. What is the constant of variation?
a)
k = 123
b)
k = 20
c)
k = 6.15
d)
k = 0.16
23.
In a direct variation, y = 39 when x = 3.
Find the value of y when x = 2.
Find the value of y when x = 2.
a)
26
b)
3
c)
58.5
d)
2
24.
What ordered pair does a direct variation always go through when graphed?
a)
(0, 0)
b)
(1, 0)
c)
(0, 1)
d)
(1, 1)
25.
Ounces of medication vary directly with the weight of the patient. If a 120-pound adult requires 3 ounces of a medication, how many ounces would be needed for a 200-pound adult?
a)
2
b)
3
c)
5
d)
9
26.
Is the given table a direct variation? If so, what is the constant of variation?
a)
Yes; 1/3
b)
Yes; 3
c)
Yes; 5
d)
No
27.
Which of the given graphs is a direct variation?
a)
A
b)
B
c)
C
d)
D
28.
What kind of equation is this?
xy=8
xy=8
a)
Linear Equation
b)
Direct Variation
c)
Inverse Variation
d)
Joint Variation
29.
Is the given table a direct or inverse variation? What is the constant of variation?
a)
Direct, 12
b)
Inverse, 12
c)
Direct, 1/12
d)
Inverse, 1/12
30.
What does the Direct Variation Equation look like?
a)
y= kx
b)
y = mx + b
c)
y = b
d)
y = x
31.
Is the given table a direct variation? If so, what is the constant of variation?
a)
Yes; 1/3
b)
Yes; 3
c)
Yes; 5
d)
No
32.
Which of the given graphs is a direct variation?
a)
A
b)
B
c)
C
d)
D
33.
What kind of equation is this?
xy=8
xy=8
a)
Linear Equation
b)
Direct Variation
c)
Inverse Variation
d)
Joint Variation
34.
Is the given table a direct variation? If so, what is the constant?
a)
Yes; 1/4
b)
Yes; 4
c)
Yes; 2
d)
No
35.
Determine the type of variation:
a)
Direct
b)
Inverse
c)
Neither
36.
What ordered pair does a direct variation always go through when graphed?
a)
(0, 0)
b)
(1, 0)
c)
(0, 1)
d)
(1, 1)
37.
What is the constant (k) in this inverse variation?
a)
12
b)
24
c)
48
d)
Not enough information given
38.
What is the constant (k) in this inverse variation?
y = 400/x
y = 400/x
a)
x
b)
y
c)
400
d)
Not enough information given
39.
a)
direct variation
b)
inverse variation
c)
neither direct nor inverse variation
40.
a)
direct variation
b)
inverse variation
c)
neither direct nor inverse variation
41.
The equation
xy = 25 represents:
xy = 25 represents:
a)
direct variation
b)
inverse variation
c)
joint variation
d)
none of these
42.
What kind of equation is this?
xy=8
xy=8
a)
Linear Equation
b)
Direct Variation
c)
Inverse Variation
d)
Joint Variation
43.
Which of the following represents direct variation?
a)
y = kx
b)
y = k/x
c)
y = x/k
d)
y = mx + b
44.
Which of the following represents indirect variation?
a)
y = kx
b)
y = k/x
c)
y = x/k
d)
y = mx + b
45.
a)
direct variation
b)
inverse variation
c)
neither direct nor inverse variation
46.
a)
direct variation
b)
inverse variation
c)
neither direct nor inverse variation
47.
a)
direct variation
b)
inverse variation
c)
neither direct nor inverse variation
48.
The equation
xy = 25 represents:
xy = 25 represents:
a)
direct variation
b)
inverse variation
c)
joint variation
d)
none of these
49.
Suppose y varies inversely with x.
If y = 150 when x = 2, find y when x = 25.
If y = 150 when x = 2, find y when x = 25.
a)
300
b)
75
c)
1,875
d)
12
50.
Which of the following represents direct variation?
a)
y = kx
b)
y = k/x
c)
y = x/k
d)
y = mx + b
51.
Is the given table a direct variation? If so, what is the constant of variation?
a)
Yes; 1/3
b)
Yes; 3
c)
Yes; 5
d)
No
52.
Which of the given graphs is a direct variation?
a)
A
b)
B
c)
C
d)
D
53.
Is the given table a direct or inverse variation? What is the constant of variation?
a)
Direct, 12
b)
Inverse, 12
c)
Direct, 1/12
d)
Inverse, 1/12
54.
Trina's paycheck earnings varies directly as the number of hours she works. If she works 19 hours and earns $187.15, what should she earn if she worked 40 hours?
a)
$394
b)
$443.25
c)
$472.80
d)
$512.20
55.
Write an equation for this relationship.
a)
y=4x
b)
y=1/8x
c)
y=1/4x
d)
y=8x
56.
Is the given table a direct variation? If so, what is the constant?
a)
Yes; 1/4
b)
Yes; 4
c)
Yes; 2
d)
No
57.
Is this a direct variation?
y=2x
y=2x
a)
yes
b)
no
58.
Which table represents a direct variation?
a)
b)
c)
d)
59.
Which equation represents an inverse variation?
a)
y=−3x+5
b)
y=−2x
c)
y=8x
d)
y=x8
60.
Which equation represents a direct variation?
a)
y=−21x+5
b)
y=−2x
c)
xy=25
d)
y=x3
61.
Y varies directly to x. If y = 16 when x = 4, which equation represents this situation?
a)
y=41x
b)
y=12x
c)
y=4x
d)
y=64x
62.
The amount of money earned on a job is directly proportional to the number of hours worked. If $70.00 is earned in 5 hours, how much money is earned in 22 hours of work?
a)
$2
b)
$308
c)
$1.57
d)
$265
63.
Given that y varies inversely with x, if x =7 and y = 4, what is y when x = 2?
a)
14
b)
10
c)
2
d)
-14
64.
The value of y varies directly with x. Which function represents the relationship between x and y if y = 14 when x = 6.
a)
y=20x
b)
y=84x
c)
y=7/3x
d)
y=3/7x
65.
Determine the type of variation:
a)
Direct
b)
Inverse
c)
Neither
66.
Y varies directly with x, and y is 84 when x is 16. Which equation represents this situation?
a)
y=1344x
b)
y=100x
c)
y=5.25x
d)
y=4/21x
67.
Is the given table a direct variation? If so, what is the constant of variation?
a)
Yes; 1/3
b)
Yes; 3
c)
Yes; 5
d)
No
68.
Which of the given graphs is a direct variation?
a)
A
b)
B
c)
C
d)
D
69.
What kind of equation is this?
xy=8
xy=8
a)
Linear Equation
b)
Direct Variation
c)
Inverse Variation
d)
Joint Variation
70.
Is the given table a direct or inverse variation? What is the constant of variation?
a)
Direct, 12
b)
Inverse, 12
c)
Direct, 1/12
d)
Inverse, 1/12
71.
The number of hours to paint a house varies inversely with the number of painters working. A 2400-square foot house can be painted in 27 hours by 6 painters. How many painters would need to work in order to paint the house in 18 hours?
a)
8 painters
b)
10 painters
c)
9 painters
d)
11 painters
72.
Boyle’s Law states that, for a fixed amount of gas, the volume of the gas at a constant temperature is inversely proportional to the pressure. If a certain gas occupies 9.84 liters at a pressure of 50 centimeters of mercury (cm Hg), what is the approximate pressure when the volume is increased to 12 liters?
a)
39.8 cm Hg
b)
41.0 cm Hg
c)
43.2 cm Hg
d)
45.1 cm Hg
73.
The time it takes to fly from Los Angeles to New York varies inversely as the speed of the plane. If the trip takes 6 hours at 900 km/h, how long would it take at 800 km/h?
a)
5.33 hours
b)
6.75 hours
c)
12 hours
d)
10 hours
74.
Trina's paycheck earnings varies directly as the number of hours she works. If she works 19 hours and earns $187.15, what should she earn if she worked 40 hours?
a)
$394
b)
$443.25
c)
$472.80
d)
$512.20
75.
The gas pressure in a chamber varies directly with the temperature in the chamber. If the pressure in the chamber is 150 atmospheres (atm) when the chamber is at 50 degrees, what is the pressure in the chamber when the temperature of the chamber is 75 degrees?
a)
175 atm
b)
200 atm
c)
225 atm
d)
275 atm
76.
Directions: Plot the other points. The coordinates of the points must be integers.
Point A is an element of a direct variation. Plot two points, other than A , that are elements of this direct variation. The coordinates of the points must be integers.
4 lines
77.
In which table does y vary directly with x ?
a)
b)
c)
d)
78.
This relation is an inverse relation.
{(−1,8),(4,−2),(−2,4)} . Which equation represents this relation?
a)
y=−3x+5
b)
y=−2x
c)
y=−8x
d)
y=−x8
79.
Directions: Plot the other points. The coordinates of the points must be integers.
The graph of the equation representing a direct variation passes through point A . Locate one additional point that is on the graph of this equation.
4 lines
80.
Two relationships are described.
Relationship S: Karen drove 160 miles in 4 hours, and then she drove 80 miles in 2 hours.
Relationship T: Vernon cooked 6 hamburgers in 10 minutes, and then he cooked 9 hamburgers in 15 minutes.
Which statement is true about these relationships?
a)
Neither relationship is a direct variation.
b)
Both relationships are direct variation.
c)
Only Relationship S is a direct variation.
d)
Only Relationship T is a direct variation.
81.
If y varies inversely as x and x=5 when y=20, then what is the constant of variation, k?
a)
121
b)
4
c)
100
d)
6
82.
If y varies directly as x and y = 24, when x = 3, then what is the value of k?
a)
4
b)
6
c)
8
d)
72
83.
Which of the given graphs is a direct variation?
a)
A
b)
B
c)
C
d)
D
84.
What ordered pair does a direct variation always go through when graphed?
a)
(0, 0)
b)
(1, 0)
c)
(0, 1)
d)
(1, 1)
85.
If x and y vary directly, what is the missing value in the points (x, 4) and (-14, -8)?
a)
x = -7
b)
x = -2.3
c)
x = 2.3
d)
x = 7
86.
The value of y varies directly with x. Which function represents the relationship between x and y if y = 14 when x = 6.
a)
y=20x
b)
y=84x
c)
y=7/3x
d)
y=3/7x
87.
a)
A
b)
B
c)
C
d)
D
88.
In a direct variation, y=39 when x=3. Find the value of y when x=2.
a)
26
b)
3
c)
58.5
d)
2
89.
y varies directly with x, and y is 16 when x is 32. Which equation represents this situation?
a)
y=32x
b)
y=16x
c)
y=2x
d)
y=(1/2)x
90.
y varies inversely with x. If y = -4 when x = 5, find y when x = 3.
a)
-20/3
b)
12/5
c)
20/3
d)
-12/5
91.
Which of the given graphs is a direct variation?
a)
A
b)
B
c)
C
d)
D
92.
Which equations represent a direct variation?
a)
y=2x
b)
xy=2
c)
y=2/x
d)
y/x=2
93.
Which equations represent an inverse variation?
a)
y=2x
b)
xy=2
c)
y=2/x
d)
y/x=2
94.
Given the table, determine if it represents a direct variation, inverse variation, or neither.
a)
Direct Variation
b)
Inverse Variation
c)
Neither
95.
Y varies directly with x, and y is 84 when x is 16. Which equation represents this situation?
a)
y=1344x
b)
y=100x
c)
y=5.25x
d)
y=4/21x
96.
Y varies inversely with x, and y is 0.5 when x is 4. Which equation represents this situation?
a)
y=2x
b)
y=2/x
c)
y=4x
d)
y=x/2
97.
The sales at a baseball game vary directly with the number of people attending. If sales for a game are $12,000 when 800 people attend, determine attendance if sales are $30,000
a)
1200 people
b)
1500 people
c)
2000 people
d)
2400 people
98.
The time it takes to fly from Los Angeles to New York varies inversely as the speed of the plane. If the trip takes 6 hours at 900 km/h, how long would it take at 800 km/h?
a)
5.33 hours
b)
6.75 hours
c)
12 hours
d)
10 hours
99.
Determine if the following graph is a direct, inverse, or neither variation.
a)
Direct Variation
b)
Inverse Variation
c)
Neither
100.
Determine if the following graph is a direct, inverse, or neither variation.
a)
Direct Variation
b)
Inverse Variation
c)
Neither
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