Deck 4: Linear Functions and Inequalities in Two Variables

Question 1

Graph the ordered pairs below. and

A)
B)
C)
D)
E)

Answer 1

Question 2

Find the coordinates of the point below.

A)
B)
C)
D)
E)

Answer 2

Question 3

Graph:

A)
B)
C)
D)
E)

Answer 3

Question 4

Graph the ordered pairs below. and

A)
B)
C)
D)
E)

Question 5

Find the coordinates of the point below.

A)
B)
C)
D)
E)

Question 6

The number of years of previous work experience and the monthly salary of a person who completes a bachelor's degree in economics are recorded in the following table. Graph the scatter diagram of these data.

A)
B)
C)
D)
E)

Question 7

Name the abscissa of the point shown below.

A) 3
B) -3
C) -2
D) 2
E)

Question 8

Sherlock Holmes solved a crime by recognizing a relationship between the length, in inches, of a person's stride and the height of that person in inches. The data for six people are recorded in the table below. Graph the scatter diagram of these data.

A)
B)
C)
D)
E)

Question 9

Is (-3, 2) a solution of ?

A) No
B) Yes

Question 10

Find the domain and range of the following function.

A) D: {-3, -2, 3, 6, 7}; R: {3, 6, 7}
B) D: R:
C) D: {3, 6, 7}; R: {3, 6, 7}
D) D: {3, 6, 7}; R: {-3, -2, 3, 6, 7}
E) D: {-3, -2, 3, 6, 7}; R: {-3, -2, 3, 6, 7}

Question 11

Graph the ordered pairs below. and

A)
B)
C)
D)
E)

Question 12

Name the abscissa of the point below.

A) 1
B) -1
C) 2
D) -2
E) 0

Question 13

Name the ordinate of the point below.

A) -2
B) 2
C) -1
D) 3
E) 1

Question 14

Is (-2, -10) a solution of ?

A) Yes
B) No

Question 15

In which quadrant does the given point lie?

A) Quadrant II
B) Quadrant III
C) Quadrant IV
D) Quadrant I
E) None of these

Question 16

Find the coordinates of the point below.

A)
B)
C)
D)
E)

Question 17

The scatter diagram below shows the record times for races of different lengths at a junior high school track meet, where x is the length of the race in meters and y is the time of race in seconds. Suppose the school adds a 500-meter race. How will that change the scatter plot? Will the graph have the same number of points or an additional point?

A) The point will be graphed with an x-coordinate of 500 and a y-coordinate equal to the record time for the 500-meter race. The graph will not have an additional point.
B) The point will be graphed with an x-coordinate of 500 and a y-coordinate equal to the record time for the 500-meter race. The graph will have an additional point.
C) The point will be graphed with an x-coordinate equal to the record time for the 500-meter race and a y-coordinate of 500. The graph will have an additional point.
D) The point will be graphed with an x-coordinate equal to the record time for the 500-meter race and a y-coordinate of 500. The graph will not have an additional point.
E) The point will be graphed with an x-coordinate of 500 and a y-coordinate of 500. The graph will not have an additional point.

Question 18

Find the coordinates of the point below.

A)
B)
C)
D)
E)

Question 19

In which quadrant does the given point lie?

A) Quadrant II
B) Quadrant I
C) None of these
D) Quadrant IV
E) Quadrant III

Question 20

The scatter diagram below pairs numbers of children with the number of households in a certain neighborhood who have that number of children. If the next household that moves in has 2 children, how will that change the scatter diagram? Will the graph have the same number of points or one additional point?

A) The point at x = 2 will move to
B) The point at x = 8 will move to
C) The graph will have a new point at
D) The graph will have a new point at
E) The point at x = 2 will move to

Question 21

A real estate appraiser charges a fee that depends on the estimated value, V, of the property. A table giving the fees charged for various estimated values of the real estate appears below. Value of Property
Appraisal Fee $350 $525 $950 $2500 $3000
A. Evaluate this function when V = $437,000.
B. Evaluate this function when V = $9,000,000.

A) (a) $525; (b) $3000
B) (a) $3000; (b) $525
C) (a) $500,000; (b) $10,000,000
D) (a) $950; (b) $3500
E) (a) $525; (b) $525

Question 22

What values are excluded from the domain of the function ?

A) 3, -3
B) 0, -3
C) -3
D) 0
E) 3

Question 23

Does the diagram below represent a function?

A) Insufficient information
B) Yes
C) No

Question 24

What values are excluded from the domain of the function ?

A) 5
B) 0
C)
D)
E) None

Question 25

Graph:

A)
B)
C)

Question 26

Given the function , find

A) 7
B) 29
C) 5
D) 30
E) 8

Question 27

State whether the following relation is a function.

A) Not a function
B) Insufficient information
C) Function

Question 28

State whether the following relation is a function.

A) Insufficient information
B) Function
C) Not a function

Question 29

What values are excluded from the domain of the function ?

A) 0, 4
B)
C) 9
D) 4
E) 4 , 9

Question 30

Graph:

A)
B)
C)

Question 31

What values are excluded from the domain of the function ?

A) 0, 2
B) 2
C) 1, 2
D) 0
E) 1

Question 32

Graph:

A)
B)
C)

Question 33

What values are excluded from the domain of the function ?

A) 4
B) 4, -3
C) 4, -4
D) 0
E) -3

Question 34

Given , write in simplest form.

A)
B)
C)
D)
E)

Question 35

What values are excluded from the domain of the function ?

A) 9
B) None
C) 3
D) 4.5
E) 0

Question 36

Given the function , find

A) 6
B) 9
C) 0
D) 3
E) -1

Question 37

Find the range of the function defined by the equation and the given domain.

A) {2}
B) all numbers
C) {-8, -4, 0, 8}
D) {(-8,146), (-4,42), (0,2), (8,114)}
E) {146, 42, 2, 114}

Question 38

Graph:

A)
B)
C)

Question 39

What values are excluded from the domain of the function ?

A)
B) 0
C) None
D)
E) 7

Question 40

Does the diagram below represent a function?

A) Insufficient information
B) Yes
C) No

Question 41

The graph below shows how the amount of fuel in the tank of a car decreases as the car is driven. Find the slope of the line between the two points shown on the graph, namely (50, 15) and (150, 9). Write a sentence that states the meaning of the slope.

A) m = -0.06; For each 100 miles the car is driven, approximately 0.06 gal of fuel is used.
B) m = -0.06; For each mile the car is driven, approximately 0.06 gal of fuel is used.
C) m = -0.06; The car averages approximately 60 miles per gallon.
D) m = 0.06; For each mile the car is driven, approximately 0.06 gal of fuel is used.
E) m = -0.6; For each mile the car is driven, approximately 0.6 gal of fuel is used.

Question 42

Graph by using the slope and y-intercept:

A)
B)
C)

Question 43

Find the slope of the line containing the given points.

A)
B) 2
C) Undefined
D) -2
E) -10

Question 44

Graph by using the slope and y-intercept:

A)
B)
C)

Question 45

The graph below shows the relationship between the distance traveled by a motorist and the time of travel. Find the slope of the line between the two points shown on the graph, namely (1, 80) and (3, 240). Write a sentence that states the meaning of the slope.

A) m = 80; The distance traveled by the motorist in 2 hours is 80 miles.
B) m = 240; The average speed of the motorist is 240 mph.
C) m = 80; The average speed of the motorist is 80 mph.
D) m = 160; The average speed of the motorist is 160 mph.
E) m = 60; The average speed of the motorist is 60 mph.

Question 46

The graph below shows the relationship between the temperature (degrees Fahrenheit) inside an oven and the time since the oven was turned off. Find the slope of the line between the two points shown on the graph, namely (20, 275) and (50, 125). Write a sentence that states the meaning of the slope.

A) m = -5; The temperature of the oven decreases 5 °/min.
B) m = -6; The temperature of the oven decreases 6 °/min.
C) m = 5; The temperature of the oven increases 5 °/min.
D) m = -150; The temperature of the oven decreases 150 °/min.
E) m = 5; The temperature of the oven decreases 5 °/min.

Question 47

Find the slope of the line containing the given points.

A)
B) -4
C)
D)
E)

Question 48

Find the equation of the line that contains the given point and has the given slope. (5, 1) , m = .

A)
B)
C)
D)
E)

Question 49

Find the equation of the line that contains the given point and has the given slope. (-2, -12) , m = 5.

A)
B)
C)
D)
E)

Question 50

Graph by using the slope and y-intercept:

A)
B)
C)

Question 51

The graph below shows the number of gallons of water remaining in a pool x minutes after a pump is turned on to drain the pool. Find the slope of the line between the two points shown on the graph, namely (0, 32) and (25, 5). Write a sentence that states the meaning of the slope.

A) m = -1.08; Each minute, 1080 gallons are being drained from the pool.
B) m = -1.08; Each minute, 1.08 gallons are being drained from the pool.
C) m = -0.93; Every 25 minutes, 930 gallons are being drained from the pool.
D) m = -1.08; Every 25 minutes, 1080 gallons are being drained from the pool.
E) m = -0.93; Each minute, 930 gallons are being drained from the pool.

Question 52

Graph:

A)
B)
C)

Question 53

Graph:

A)
B)
C)

Question 54

A custom-illustrated sign or banner can be commissioned for a cost of $21.00 for the material and $11.90 per square foot for artwork. The equation that represents this cost is given by y = 11.90x + 21.00, where y is the cost and x is the number of square feet in the sign. When this equation is graphed for , the ordered pair (13, 175.70) is discovered to lie on the graph. Write a sentence that describes the meaning of the ordered pair (13, 175.70).

A) It costs $175.70 for each additional square foot of sign area.
B) It costs $13 for a custom sign 175.70 ft² in area.
C) It costs $13 for material and $175.70 for artwork.
D) It costs $175.70 for a custom sign 13 ft² in area.
E) It costs $13 for each additional square foot of sign area.

Question 55

Find the x- and y-intercepts of the line

A) x-intercept: (9, 0), y-intercept: (0, -6)
B) x-intercept: (-9, 0), y-intercept: (0, 6)
C) x-intercept: (6, 0), y-intercept: (0, 9)
D) x-intercept: (9, 0), y-intercept: (0, 6)
E) x-intercept: (-9, 0), y-intercept: (0, -6)

Question 56

Graph:

A)
B)
C)

Question 57

Graph by using the slope and y-intercept:

A)
B)
C)

Question 58

Graph by using the slope and y-intercept:

A)
B)
C)

Question 59

Find the equation of the line that contains the given point and has the given slope. (-4, 21) , m = -4.

A)
B)
C)
D)
E)

Question 60

Graph by using the slope and y-intercept:

A)
B)
C)

Question 61

The slope of a line is . What is the slope of any line perpendicular to this line?

A)
B)
C)
D)
E)

Question 62

Let f be a linear function. If and , find .

A)
B)
C)
D)
E)

Question 63

A Boeing 747 jet takes off from Boston's Logan Airport, which is at sea level, and climbs to a cruising altitude of 27,000 ft at a constant rate of 1100 ft/min.

A. Write a linear equation for the height of the plane in terms of the time after takeoff.
B. Use your equation to find the height of the plane 12 min after takeoff.

A) (a) ; (b) 13,800 ft
B) (a) ; (b) 40,200 ft
C) (a) ; (b) 13,200 ft
D) (a) ; (b) 40,200 ft
E) (a) ; (b) 13,200 ft

Question 64

Find the equation of the line passing through the points whose coordinates are .

A)
B)
C)
D)
E)

Question 65

Is the line parallel to the line ?

A) Insufficient information
B) Yes
C) No

Question 66

An account executive receives a base salary plus a commission. With $17,000 in monthly sales, the account executive receives $1700. On $45,000 in monthly sales, the account executive receives $2700.
A. Determine a linear function that will yield the compensation of the sales executive for a given amount of monthly sales. Round any numbers in your function to the nearest hundredth.
B. Use this model, with coefficients rounded to the nearest hundreth, to determine the account executive's compensation for $36,700 in monthly sales. Round to the nearest dollar.

A) (a) ; (b) $1468
B) (a) ; (b) $1093
C) (a) ; (b) $4763
D) (a) ; (b) $2561
E) (a) ; (b) $1468

Question 67

The gas tank of a certain car contains 17 gal of gas when the driver of the car begins a trip. Each mile driven by the driver decreases the amount of gas in the tank by 0.068 gal.
A. Write a linear function for the number of gallons of gas in the tank in terms of the number of miles driven.
B. Use your equation to find the number of gallons in the tank after driving 161 mi. Round your answer to the nearest tenth of a gallon.

A) (a) ; (b) 27.9 gal
B) (a) ; (b) 27.9 gal
C) (a) ; (b) 6.1 gal
D) (a) ; (b) 10.9 gal
E) (a) ; (b) 10.9 gal

Question 68

Find the equation of line that contains the point whose coordinates are (-7, -10) and whose slope is undefined.

A)
B)
C)
D)
E)

Question 69

Find the equation of the line passing through the points whose coordinates are .

A)
B)
C)
D)
E)

Question 70

The slope of a line is . What is the slope of any line parallel to this line?

A)
B)
C)
D)
E)

Question 71

Find the equation of the line that contains the points P₁(-2, -8) and P₂(-2, 8).

A)
B)
C)
D)
E)

Question 72

Is the line perpendicular to the line ?

A) Insufficient information
B) Yes
C) No

Question 73

Find the equation of the line that contains the given point and has the given slope. (-5, -6) , m =

A)
B)
C)
D)
E)

Question 74

Find the equation of the line that contains the points P₁(-2, -4) and P₂(3, -7).

A)
B)
C)
D)
E)

Question 75

A cellular phone company offers several different service plans. One option, for people who plan on using the phone only in emergencies, costs the user $5.15 per month plus $0.60 per minute for each minute the phone is used.
A. Write a linear function for the monthly cost of the phone in terms of the number of minutes the phone is used.
B. Use your equation to find the cost of using the cellular phone for 14 minutes in 1 month.

A) (a) ; (b) $8.40
B) (a) ; (b) $19.15
C) (a) ; (b) $13.55
D) (a) ; (b) $5.15
E) (a) ; (b) $72.70

Question 76

Find the equation of the line that contains the points P₁(-3, -4) and P₂(5, -4).

A)
B)
C)
D)
E)

Question 77

A manufacturer of graphing calculators has determined that 12,000 calculators per week will be sold at a price of $110 each. At a price of $90, it is estimated that 15,000 calculators would be sold.

A. Determine a linear function that will predict the number of calculators that would be sold at a given price, x.
B. Use this model to predict the number of calculators that would be sold each week at a price of $75.

A) (a) ; (b) 13,500 calculators
B) (a) ; (b) 6750 calculators
C) (a) ; (b) 751 calculators
D) (a) ; (b) 17,250 calculators
E) (a) ; (b) 17,250 calculators

Question 78

Find the equation of the line passing through the points whose coordinates are .

A)
B)
C)
D)
E)

Question 79

Given that f is a linear function for which and , determine .

A) 1
B) 19
C) -3
D) 3
E) 5

Question 80

Find the equation of the line passing through the points whose coordinates are .

A)
B)
C)
D)
E)