Deck 1: Linear Functions

Question 1

Why is the slope of a vertical line undefined?

Answer 1

Question 2

When going more than 38 miles per hour, the gas mileage of a certain car fits the model $y=43.81-0.395 x$ where $x$ is the speed of the car in miles per hour and $y$ is the miles per gallon of gasoline. Based on this model, at what speed will the car average 15 miles per gallon? (Round to nearest whole number.)

A) 98 miles per hour
B) 73 miles per hour
C) 48 miles per hour
D) 149 miles per hour

Answer 2

73 miles per hour

Question 3

Solve the problem.

Answer 3

B

Question 4

Find an equation in slope-intercept form (where possible) for the line.

Question 5

Graph the equation.
y + 2 = 0

Question 6

Can an equation of a vertical line be written in slope-intercept form? Explain.

Question 7

Give a definition or an example of the word or phrase: Zero slope

Question 8

A study was conducted to compare the average time spent in the lab each week versus course grade for computer students. The results are recorded in the table below. Use the equation of the
Least squares line to predict the grade of a student who spends 5 hours in the lab.

A) $80.3 \%$
B) $75.3 \%$
C) $79.3 \%$
D) $83.6 \%$

Question 9

Find the correlation coefficient.
The following are the temperatures on randomly chosen days and the amount a certain kind of plant grew (in millimeters):

Question 10

John has been a teacher at West Side High School for the past 12 years. His salary during that time can be modeled by the linear equation y = 800x + 33,000 where x is the number of years since he began teaching at West Side and y is his salary in dollars. Explain what the slope, 800, represents in this context.

Question 11

If a company decides to make a new product, there are fixed costs and variable costs
associated with this new product. Explain the differences of the two types of costs and
why they occur. Use an example to illustrate your point.

Question 12

Find the correlation coefficient.

Question 13

Question 14

Solve the problem.

Question 15

Find the equation of the least squares line.

-Ten students in a graduate program were randomly selected. Their grade point averages (GPAs) when they entered the program were between 3.5 and 4.0. The following data were obtained Regarding their GPAs on entering the program versus their current GPAs.

A) $y=3.67+0.0313 x$
B) $y=4.91+0.0212 x$
C) $y=2.51+0.329 x$
D) $y=5.81+0.497 x$

Question 16

Graph the equation.
5y + 2x = -15 11)

Question 17

The total number of reported cases of AIDS in the United States has risen from 372 in 1981 to 100,000 in 1989 and 200,000 in 1992. Does a linear equation fit this data? Explain.

Question 18

Why is the slope of a horizontal line equal to zero? Give an example.

Question 19

Graph the equation.
y = -6

Question 20

Explain what is wrong with the statement "The line has no slope.

Question 21

Solve the problem.

-The information in the chart gives the salary of a person for the stated years. Model the data with a linear function using the points (1, 24,100)and (3, 26,800).

A) $y=1350 x+22,750$
B) $y=-1591 x+22,750$
C) $y=29.5 x+22,750$
D) $y=1350 x$

Question 22

Find an equation in slope-intercept form (where possible) for the line.

Question 23

Evaluate the function as indicated.

Question 24

Find the correlation coefficient.
The following are the temperatures on randomly chosen days and the amount a certain kind of plant grew (in millimeters):

Question 25

Provide an appropriate response.

Question 26

Find the correlation coefficient.
The test scores of 6 randomly picked students and the number of hours they prepared are as follows:

Question 27

Solve the problem.

Question 28

Find an equation in slope-intercept form (where possible) for the line.

Question 29

Find an equation in slope-intercept form (where possible) for the line.

Question 30

Evaluate the function as indicated.

Question 31

Solve the problem.
Given the supply and demand functions below, find the demand when p = $12.

Question 32

Evaluate the function as indicated.

Question 33

Find the correlation coefficient.

-The test scores of 6 randomly picked students and the number of hours they prepared are as follows:

A) $0.2015$
B) $-0.2241$
C) $-0.6781$
D) $0.6039$

Question 34

Solve the problem.

-For some reason the quality of production decreases as the year progresses at a light bulb manufacturing plant. The following data represent the percentage of defective light bulbs Produced at a light bulb manufacturing plant in the corresponding month of the year. Use the equation of the least squares line to predict in which month the percentage of defective
Light bulbs would be 1.83%.

A)February
B)May
C)March
D)April

Question 35

Evaluate the function as indicated.

Question 36

Find the slope of the line.
The x-axis

A)0
B)-1
C)Not defined
D)1

Question 37

Solve the problem.

-In a certain city, the cost of a taxi ride is computed as follows: There is a fixed charge of $2.45 as soon as you get in the taxi, to which a charge of $2.05 per mile is added. Find a linear equation that Can be used to determine the cost, C, of an x-mile taxi ride.

A)C = 4.50x
B)C = 3.00x
C)C = 2.05x + 2.45
D)C = 2.45x + 2.05

Question 38

Graph the equation.
y = 3x - 2

Question 39

Solve the problem.

-For some reason the quality of production decreases as the year progresses at a light bulb manufacturing plant. The following data represent the percentage of defective light bulbs Produced at a light bulb manufacturing plant in the corresponding month of the year. Use the equation of the least squares line to predict the percentage of defective bulbs in June.

A)2.0%
B)2.3%
C)2.20%
D)2.15%

Question 40

Graph the equation.

-2y - 7x = 4

A)
B)
C)
D)

Question 41

Solve the problem.

-The change in a certain engineer's salary over time can be approximated by the linear equation y = 1500x + 47,500 where y represents salary in dollars and x represents number of years on the job.According to this equation, after how many years on the job was the engineer's salary $64,000?

A)13 years
B)11 years
C)12 years
D)10 years

Question 42

Find an equation in slope-intercept form (where possible) for the line.

Question 43

Find the slope of the line.

Question 44

Find an equation in slope-intercept form (where possible) for the line.

Question 45

Solve the problem.

-Midtown Delivery Service delivers packages which cost $1.10 per package to deliver. The fixed cost to run the delivery truck is $60 per day. If the company charges $7.10 per package, how many Packages must be delivered daily to break even?

A)54 packages
B)7 packages
C)10 packages
D)6 packages

Question 46

Find the equation of the least squares line.

-Two different tests are designed to measure employee productivity and dexterity. Several employees of a company are randomly selected and asked to complete the tests. The results are Below.

A) $y=75.3-0.329 x$
B) $y=10.7+1.53 x$
C) $y=5.05+1.91 x$
D) $y=2.36+2.03 x$

Question 47

Solve the problem.

-The cost of owning a home includes both fixed costs and variable utility costs. Assume that it costs $5682 per month for mortgage and insurance payments and it costs an average of $1.35 per unit for Natural gas, electricity, and water usage. Determine a linear equation that computes the annual cost Of owning this home if x utility units are used.

A)y = -1.35x + 68,184
B)y = 1.35x + 5682
C)y = -1.35x + 5682
D)y = 1.35x + 68,184

Question 48

Evaluate the function as indicated.

-Find f(5.2)when f(x)= 7

A)5.2
B)36.4
C)7
D)-7

Question 49

Evaluate the function as indicated.

Question 50

Solve the problem.
Find the temperature at which the Celsius and Fahrenheit scales coincide.

A)-25°
B)0°
C)-40°
D)39°

Question 51

Graph the equation.
5x + y = -4

Question 52

Find the slope of the line.

Question 53

Find the slope of the line passing through the given pair of points.

Question 54

Find an equation in slope-intercept form (where possible) for the line.

Question 55

Write a cost function for the problem. Assume that the relationship is linear.
A moving firm charges a flat fee of $40 plus $35 per hour. Let C(x)be the cost in dollars of using the moving firm for x hours.

A)C(x)= 40x + 35
B)C(x)= 35x + 40
C)C(x)= 35x - 40
D)C(x)= 40x - 35

Question 56

Find an equation in slope-intercept form (where possible) for the line.

Question 57

Find an equation in slope-intercept form (where possible) for the line.

Question 58

Solve the problem.
A car rental company charges $33 per day to rent a particular type of car and $0.15 per mile. Juan is charged $56.70 for a one-day rental. How many miles did he drive?

A)173 mi
B)158 mi
C)345 mi
D)378 mi

Question 59

Solve the problem.

-For the following table of data,
a. Draw a scatterplot.
B. Calculate the correlation coefficient.
C. Calculate the least squares line and graph it on the scatterplot.
D. Predict the y-value when x is 11.

A)
B)
C)

D)

Question 60

Solve the problem.

-The paired data below consist of the costs of advertising (in thousands of dollars)and the number of products sold (in thousands). Use the equation of the least squares line to predict the number of Products sold if the cost of advertising is $6000.

A)72.54 products sold
B)69.54 products sold
C)16,795.8 products sold
D)79.24 products sold

Question 61

Solve the problem.

-Northwest Molded molds plastic handles which cost $1.00 per handle to mold. The fixed cost to run the molding machine is $5616 per week. If the company sells the handles for $4.00 each, how many Handles must be molded weekly to break even?

A)5616 handles
B)1248 handles
C)1872 handles
D)1123 handles

Question 62

For the following table of data,
A. Draw a scatterplot.
B. Calculate the correlation coefficient.
C. Calculate the least squares line and graph it on the scatterplot.
D. Predict the y-value when x is -19.

A)

B)

C)
D)

Question 63

Suppose that the demand and price for a certain model of graphing calculator are related by $p=D(q)=96-1.5 q$ , where $p$ is the price (in dollars) and $q$ is the demand (in hundreds). Find the price if the demand is 600 calculators.

A) $\$ 105.00$
B) $\$ 87.00$
C) $\$ 6.00$
D) $\$ 186.00$

Question 64

Evaluate the function as indicated.

Question 65

Suppose that the population of a certain town, in thousands, was 105 in 1990 and 141 in 2002. Assume that the population growth can be approximated by a straight line. Find the equation of a Line which will estimate the population of the town, in thousands, in any given year since 1990.

A)y = 4.25x + 90 where x is the number of years since 1990
B)y = 3x + 105 where x is the number of years since 1990
C)y = 2.5x + 105 where x is the number of years since 1990
D)y = -3x + 177 where x is the number of years since 1990

Question 66

Find an equation in slope-intercept form (where possible) for the line.

Question 67

Find the slope of the line passing through the given pair of points.

Question 68

A biologist recorded 9 snakes on 14 acres in one area and 18 snakes on 21 acres in another area. Let y be the number of snakes in x acres. Write a linear equation for the number of snakes.

A) $y=\frac{9}{7} x+9$
B) $y=-\frac{9}{7} x+9$
C) $y=\frac{7}{9} x+9$
D) $y=\frac{9}{7} x-9$

Question 69

Let the supply and demand functions for a certain model of electric pencil sharpener be given by $p=S(q)=\frac{2}{3} q \quad$ and $p=D(q)=12-\frac{2}{3} q$ where p is the price in dollars and q is the quantity of pencil sharpeners (in hundreds). Graph these functions on the same axes (graph the supply function as a dashed line and the demand function as A solid line). Also, find the equilibrium quantity and the equilibrium price.

A)

B)

C)

D)

Question 70

Solve the problem.
The bank's temperature display shows that it is 22° Celsius. What is the temperature in Fahrenheit?

A)97.2°
B)-5.6°
C)30.0°
D)71.6°

Question 71

The paired data below consist of the test scores of 6 randomly selected students and the number of hours they studied for the test. Use the equation of the least squares line to predict the score on the Test of a student who studies 13 hours.

A)81.2
B)86.2
C)76.2
D)86.8

Question 72

Write a cost function for the problem. Assume that the relationship is linear.
A cab company charges a base rate of $1.00 plus 10 cents per minute. Let C(x)be the cost in dollars of u sing the cab for x minutes.

Question 73

Assume that the sales of a certain appliance dealer can be approximated by a straight line. Suppose that sales were $13,500 in 1982 and $65,000 in 1987. Let x = 0 represent 1982. Find the equation
Giving yearly sales S.

A)S = 51,500x + 65,000
B)S = 51,500x + 13,500
C)S = 10,300x + 65,000
D)S = 10,300x + 13,500

Question 74

Graph the equation.
x = -5

Question 75

The information in the chart below gives the salary of a person for the stated years. Model the data with a linear function using the points (1, 24,100)and (3, 26,300). Then use this function to predict The salary for the year 2005.

A) $\$ 40,000$
B) $\$ 39,980$
C) $\$ 40,040$
D) $\$ 40,020$

Question 76

The outdoor temperature rises to 22° Fahrenheit. What is this temperature in Celsius?

A)-10°
B)22°
C)-5.6°
D)12.2°

Question 77

Find the correlation coefficient.
Consider the data points with the following coordinates:

Question 78

Solve the problem.

-Find an equation for the least squares line representing weight, in pounds, as a function of height, in inches, of men. Then, predict the weight of a man who is 68 inches tall to the nearest tenth of a Pound. The following data are the (height, weight)pairs for 8 men: (66, 150), (68, 160), (69, 166),
(70, 175), (71, 181), (72, 191), (73, 198), (74, 206).

A)161.2 pounds
B)165.1 pounds
C)160.0 pounds
D)151.4 pounds

Question 79

Find the slope of the line.

Question 80

In the table below, x represents the number of years since 2000 and y represents annual sales (in thousands of dollars)for a clothing company. Use the least squares regression equation to Estimate sales in the year 2006. Round to the nearest thousand dollars.

A) $\$ 142,000$
B) $\$ 145,000$
C) $\$ 140,000$
D) $\$ 147,000$