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Direct Variation

Multiple Choice
Identify the choice that best completes the statement or answers the question.
 
 
Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.
 

 1. 

x
y
6
24
18
72
54
216
162
648
a.
yes; k = 4; y =4x
c.
yes; k = 6; y =6x
b.
yes; k = 3; y =3x
d.
no
 

 2. 

x
y
6
7.2
11
13.2
16
19.2
21
25.2
a.
yes; k = 1.2; y = 1.2x
c.
yes; k = 6
b.
yes; k = 5
d.
no
 
 
Determine whether y varies directly with x. If so, find the constant of variation k.
 

 3. 
–6y = –5x
a.
yes; mc003-1.jpg
b.
yes; mc003-2.jpg
c.
yes; –5
d.
no
 

 4. 
8y = 7x – 27
a.
yes; 8
b.
yes; 7
c.
yes; mc004-1.jpg
d.
no
 

 5. 
The range of a car is the distance R in miles that a car can travel on a full tank of gas. The range varies directly with the capacity of the gas tank C in gallons.
a.Find the constant of variation for a car whose range is 341 mi with a gas tank that holds 22 gal.
b.Write an equation to model the relationship between the range and the capacity of the gas tank.
a.
mc005-1.jpg mi/gal; R = mc005-2.jpgC
c.
mc005-5.jpg mi/gal; R = mc005-6.jpgC
b.
mc005-3.jpg mi/gal; C = mc005-4.jpgR
d.
7502 mi/gal; RC = 7502
 

 6. 
A leaky valve on the water meter overcharges the residents for one gallon of water in every mc006-1.jpg months. The overcharged amount w varies directly with time t.
a.Find the equation that models this direct variation.
b.How many months it will take for the residents to be overcharged for 8 gallons of water?
a.
mc006-2.jpg; 20 months
c.
mc006-4.jpg; mc006-5.jpg months
b.
mc006-3.jpg; 20 months
d.
mc006-6.jpg; mc006-7.jpg months
 
 
Find the value of y for a given value of x, if y varies directly with x.
 

 7. 
If y = 166 when x = 83, what is y when x = 23?
a.
11.5
b.
–11.5
c.
–46
d.
46
 

 8. 
If y = 4.8 when x = 2.4, what is y when x = 2.05?
a.
4.1
b.
1.03
c.
–1.03
d.
–4.1
 

 9. 
The distance traveled at a constant speed is directly proportional to the time of travel. If Olivia traveled 112 miles in 3.5 hours, how many miles will Olivia travel in 8.9 hours at the same constant speed?
a.
99.6 mi
b.
284.8 mi
c.
172.8 mi
d.
124.4 mi
 

 10. 
A balloon takes off from a location that is 158 ft above sea level. It rises 56 ft/min. Write an equation to model the balloon’s elevation h as a function of time t.
a.
t = 158h + 56
b.
h = 56t + 158
c.
h = 158t + 56
d.
t = 56h + 158
 



 
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