# Section 3 -2 Linear Functions

Business

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Q 3Q 3

The slope of the graph of a linear function is the same as the rate of change of the linear function.

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Q 5Q 5

You can get the rate of change of a linear function by dividing the change in the variable by the change in the function.

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Q 6Q 6

You can get the change in a linear function from the formula
Change in function = Slope × Change in variable.

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Q 7Q 7

If I add $5 to a cookie jar each week, then the amount of money in the cookie jar is a linear function of time with slope 5 dollars per week.

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Q 8Q 8

If a population doubles in size each day, then the population is a linear function of time with slope 2.

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Q 9Q 9

If snow is falling at a rate of 0.5 inch each hour, then the depth of snow on the ground is a linear function of time as long as the snow continues to fall.

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Q 11Q 11

You pay $10 to register at a web site.After registering you pay 59 cents for each song you download.Then the total amount you pay for music at this site is a linear function of the number of songs you download.

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Q 12Q 12

It is a fact that if you drop a rock, it will fall 16 feet the first second of the fall.The next second it will fall 48 feet.In view of this fact, I can conclude that the distance a rock falls is a linear function of the time since the rock was dropped.

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Q 13Q 13

It is a fact that if you drop a rock, its velocity increases by 32 feet per second for each additional second it falls.We can conclude that the velocity of the rock is a linear function of time since the rock was dropped.

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Q 14Q 14

If is increased by 5 units from , then is increased by 9 units.If is increased by an additional 5 units, then is increased by 11 units.We can conclude that a linear function of .

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Q 15Q 15

My business pays tax on income, and the tax paid is a linear function of income.If my income is $10420 then the tax owed is $929.60.If my income is $11309 then the tax owed is $1000.72.How much tax do I owe if my income is $11874?
A) $1045.92
B) $1046.18
C) $949.92
D) $950.03

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Multiple Choice

Q 16Q 16

The money I pay for music is a linear function of the number of songs I download.If I download 7 songs, then I pay $11.98.If I download 13 songs, then I pay $18.82.How much do I pay if I download 23 songs?
A) $27.16
B) $30.64
C) $26.22
D) $30.22

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Multiple Choice

Q 17Q 17

If a rock is thrown downward with an initial velocity of 8 feet per second, then its velocity , in feet per second, after seconds is given by
By how much does velocity increase over a 4-second period?
A) 32.16 feet per second
B) 128.09 feet per second
C) 32.00 feet per second
D) 128.00 feet per second

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Multiple Choice

Q 18Q 18

When you order merchandise from a web site you pay shipping costs , in dollars.The shipping costs depend on the weight , in pounds, of the merchandise.The relationship is
If my order weighs 5 pounds more than yours, how do shipping costs compare?
A) My costs are $1.87 more than yours.
B) My costs are $8.65 more than yours.
C) My costs are $8.10 more than yours.
D) My costs are $1.62 more than yours.

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Multiple Choice

Q 19Q 19

The distance , in miles, I can drive without stopping for gas depends on the amount , in gallons, of fuel in the tank.The relationship is .
If I add 5 gallons of fuel to my tank, how much farther can I drive?
A) 135.00 miles
B) 135.79 miles
C) 27.43 miles
D) 27.00 miles

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Multiple Choice

Q 20Q 20

The sales tax , in dollars, I have to pay when I buy dollars worth of merchandise is given by .
If I decide to buy $44 more in merchandise, how much additional sales tax will I have to pay?
A) $3.96
B) $4.76
C) $0.72
D) $0.09

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Multiple Choice

Q 21Q 21

I am saving money in a cookie jar.The amount of money , in dollars, in the jar after weeks is given by .
By how much do my savings grow over a 8-week period?
A) $184.29
B) $184.00
C) $23.45
D) $23.00

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Multiple Choice

Q 22Q 22

For a certain group of animals, the running speed , in feet per second, is a linear function of the length , in inches.The relationship is .
If one animal is 5 inches longer than another, how much faster does it run?
A) 10.65 feet per second
B) 10.2 feet per second
C) 2.08 feet per second
D) 2.04 feet per second

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Multiple Choice

Q 23Q 23

The life expectancy , measured in years, of a child born years after 2003 is given by .
If one child is born 5 years after another, how much greater is the life expectancy? Assume that both children are born after 2003, so the formula above applies.
A) 1.51 years
B) 0.90 years
C) 5.66 years
D) 0.18 years

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Q 24Q 24

Suppose is a linear function with and .What is the slope of ?
A) 0.5021568627
B) 3.47
C) 0.3921568627
D) 2.55

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Q 25Q 25

Suppose is a linear function with .If the slope of is 2.34, what is the value of ?
A) 23.53
B) 27.4
C) 23.4
D) 27.77

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Q 26Q 26

Suppose is a linear function with .If the slope of is 2.29, what value of gives ?
A)
B)
C)
D)

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Q 28Q 28

Suppose is a linear function with slope 2.99.Suppose further that when .Use a formula to express as a function of .
A)
B)
C)
D)

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Q 29Q 29

Suppose is a linear function of .The slope is 2.07.An increase of 7 units in causes what change in ?
A) A decrease of 14.49 units
B) An increase of 14.49 units
C) An increase of 3.3816425121 units
D) A decrease of 3.3816425121 units

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Q 30Q 30

Suppose is a linear function of .The slope is 2.89.An increase of 7 units in causes what change in ?
A) A decrease of 20.23 units
B) An increase of 20.23 units
C) An increase of 2.4221453287 units
D) A decrease of 2.4221453287 units

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Q 31Q 31

Suppose is a linear function of .The slope is 2.39.A decrease of 7 units in causes what change in ?
A) A decrease of 16.73 units
B) An increase of 16.73 units
C) An increase of 2.9288702929 units
D) A decrease of 2.9288702929 units

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Q 32Q 32

Suppose is a linear function of .The slope is 2.44.A decrease of 7 units in causes what change in ?
A) A decrease of 17.08 units
B) An increase of 17.08 units
C) An increase of 2.87 units
D) A decrease of 2.87 units

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Multiple Choice

Q 33Q 33

If a rock is thrown downward with an initial velocity of 14 feet per second, then its velocity , in feet per second, after seconds is given by .
Identify the slope, and explain in practical terms its meaning.

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Q 34Q 34

When you order merchandise from a web site you pay shipping costs , in dollars.The shipping costs depend on the weight , in pounds, of the merchandise.The relationship is .
Identify the slope, and explain in practical terms its meaning.

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Q 35Q 35

The distance , in miles, I can drive without stopping for gas depends on the amount , in gallons, of fuel in the tank.The relationship is .
Identify the slope, and explain in practical terms its meaning.

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Q 36Q 36

The sales tax , in dollars, I have to pay when I buy dollars worth of merchandise is given by .
Identify the slope, and explain in practical terms its meaning in terms of percentages.

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Q 37Q 37

I am saving money in a cookie jar.The amount of money , in dollars, in the jar after weeks is given by .
Identify the slope, and explain in practical terms what it means.

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Q 38Q 38

For a certain group of animals, the running speed , in feet per second, is a linear function of the length , in inches.The relationship is .
Identify the slope, and explain in practical terms what it means.

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Q 39Q 39

The life expectancy , measured in years, of a child born years after 2003 is given by .
Identify the slope, and explain in practical terms what it means.

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