Deck 2: Linear Equations and Inequalities With One Variable

Question 1

If the slope of one equation is and the slope of another equation is then the graphs of these equations are perpendicular.

Answer 1

False

Question 2

The slope-intercept form of the equation is:

A)
B) y = -4 x + 2
C) y = 2 x
D) y = x
E) y = 4 x

Answer 2

y = x

Question 3

The slope of the function is .

Answer 3

False

Question 4

If the gym charges $75 per month for a membership plus $35 initiation fee then the cost of the gym's monthly membership is directly proportional to the number of months the membership is active.

Question 5

If the slope of a line is m = then the change in the run is 20.

Question 6

Which one of the following graphs illustrates the equation y = 4 x ?

A)
B)
C) None of these options
D)
E)

Question 7

After taking a bath you begin to drain the water from the bathtub. The water drains at 0.5 gallon(s) per minute. After 11 minutes there are 24 gallons of water remaining. How many minutes will it take for the remaining gallons of water to drain from the tub?

A) Approximately 11 minutes
B) Approximately 22 minutes
C) Approximately 0 minutes
D) Approximately 12 minutes
E) Approximately 48 minutes

Question 8

Find the equation of a line that passes through the points and .

A) y = x +
B) y = + x
C) y = + x
D) y = x
E) y = + x

Question 9

If the price of gas is $2.35 per gallon then the cost of filling a car's tank with gas is directly proportional to the number of gallons of gas purchased.

Question 10

The owner of a gas station records the number of gallons of gas he sells over a period of time. He notices that the number of gallons of gas he sells depends linearly on the price he charges for each gallon. When he charges $1.67 per gallon of gas he sells 1000 gallons of gas each day. When he charges $2.49 per gallon he sells 600 gallons. Which one of the following equations model the number of gallons sold at price x ?

A) y = 1814.63 -488 x
B)
C)
D)
E)

Question 11

The graph of the line and the graph of the line have the same slope and thus are parallel lines.

Question 12

Find the equation of the line for the following graph.

A)
B)
C)
D) 5
E)

Question 13

Find the slope and y -intercept for the equation .

A) Slope = 8; y -intercept (0 )
B) Slope = ; y -intercept (0 )
C) Slope = ; y -intercept
D) Slope = ; y -intercept (0 )
E) Slope = 8; y -intercept

Question 14

Find the equation of a line with slope = -8 and y -intercept of 2.

A)
B)
C)
D)
E)

Question 15

Which one of the following graphs illustrates the equation ?

A)
B)
C)
D) None of these options
E)

Question 16

After taking a bath you begin to drain the water from the bathtub. The water drains at 2.5 gallons per minute. After 9 minutes there are 27 gallons of water remaining. Which one of the following linear equations describe the number of gallons of water in the tub relative to the number of minutes since you began draining the tub?

A)
B)
C)
D)
E)

Question 17

Given the graph below find the rise over run between any two points.

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

Question 18

The y -intercept of the function is .

Question 19

If the slope of a line is m = then the change in the run is 13.

Question 20

The owner of a gas station records the number of gallons of gas he sells over a period of time. He notices that the number of gallons of gas he sells depends linearly on the price he charges for each gallon. When he charges $1.77 per gallon of gas he sells 1000 gallons of gas each day. When he charges $2.32 per gallon he sells 400 gallons. How many gallons of gas would the owner sell if he charged $2.19 per gallon? (Round to the nearest whole number.)

A) 1314
B) 2389
C) 876
D) 2190
E) 542

Question 21

A beanstalk grows at a constant rate. The beanstalk s height (inches) as a function of time (days) is modeled by . At what rate is the beanstalk growing?

A) 5 inches/day
B) 0.25 inches/day
C) 5.25 inches/day
D) Not enough information
E) 1 inch/day

Question 22

A beanstalk grows at a constant rate. The beanstalk s height (inches) as a function of time (days) is modeled by . Which of the following graphs illustrate the function h ?

A)
B)
C)
D)
E) None of these options

Question 23

Using the function determine the average rate of change of the function between and .

A)
B) 95
C)
D) -1
E) 96

Question 24

Using the following graph determine the average rate of change of the function between and .

A) -15.3
B) 6.0
C) 24.0
D) 4.0
E) 8.7

Question 25

A water tank is being drained at the rate of 19 gal/min. The tank started with 16850 gallons of water. Which of the following linear functions model the number of gallons of water in the tank at any time t .

A)
B)
C)
D)
E)

Question 26

The distance d of a car traveling in a straight line is a function of the number of minutes traveled n . Using the data provided in the table for the car's distance and number of minutes determine which 10-second interval of time had the highest average rate of change.

A) from 50 minutes to 60 minutes
B) from 30 minutes to 40 minutes
C) from 0 minutes to 10 minutes
D) from 70 minutes to 80 minutes
E) from 60 minutes to 70 minutes

Question 27

The owner of a gas station records the number of gallons of gas he sells over a period of time. He notices that the number of gallons of gas he sells depends linearly on the price he charges for each gallon. When he charges $1.71 per gallon of gas he sells 800 gallons of gas each day. When he charges $2.41 per gallon he sells 400 gallons. What does the slope of the line convey about the situation?

A) None of the above
B) The price of each gallon when 800 gallons are sold.
C) The number of gallons sold decreases by 571 for each one dollar increase in price.
D) The price of each gallon per number of gallons sold.
E) The number of gallons sold at $1.71 per gallon.

Question 28

The mass of bacteria (in micrograms) in a Petri dish for different times is shown in the table below. Determine the average rate of change of the bacteria from 8:30 am to 10:30 am? (Rounded to the nearest hundredths)

A) 74.38
B) 2.00
C) 0.05
D) 36.48
E) 18.24

Question 29

A ball is thrown straight upward from a bridge and then falls all the way to the ground (past the bridge). The ball s height h (in feet) above the ground t seconds after the ball is thrown is given by . Find the average speed in the height of the ball from time seconds to seconds. (Rounded to the nearest thousandth)

A) 0.7 feet/sec
B) 125.64 feet/sec
C) -13.6 feet/sec
D) -0.074 feet/sec
E) -9.52 feet/sec

Question 30

Using the following table of values determine the average rate of change between and .

A) 3
B) 38
C)
D)
E) -14

Question 31

For the linear equation find the slope of the line.

A)
B) 8
C) -8
D)
E) 24

Question 32

A beanstalk grows at a constant rate. The beanstalk s height (inches) as a function of time (days) is modeled by . What is the beanstalk s initial height?

A) 5.5 inches
B) 5 inches
C) 0.5 inches
D) 0 inches
E) Not enough information

Question 33

Using the following graph find the slope of the line.

A) -0.2
B) 0.2
C) 5
D) 3
E) -5

Question 34

Using the following table of values determine the average rate of change between and .

A) 22
B)
C)
D) 17
E) 4

Question 35

The owner of a gas station records the number of gallons of gas he sells over a period of time. He notices that the number of gallons of gas he sells depends linearly on the price he charges for each gallon. When he charges $1.96 per gallon of gas he sells 800 gallons of gas each day. When he charges $2.65 per gallon he sells 400 gallons. Which one of the following graphs illustrate this situation?

A) None of these options
B)
C)
D)
E)

Question 36

For the linear equation find the -intercept.

A)
B)
C) ( 0)
D) ( 0)
E)

Question 37

If and then the average rate of change of between and is which of the following:

A) -7
B) 4
C)
D)
E) 7

Question 38

For the linear equation find the slope of the line.

A) 7
B) 21
C)
D)
E) -7

Question 39

The graph below shows distance as a function of time (measured in seconds) for an Olympic swimmer racing in the 100-meter butterfly. Determine the best answer for the average speed of the swimmer for the 100-meter butterfly. (Rounded to the nearest hundredth)

A) 1.39 meters/sec
B) 70 meters/sec
C) 1 meters/sec
D) 0.72 meters/sec
E) 100 meters/sec

Question 40

For the linear equation find the y -intercept.

A) (0 )
B)
C)
D) (0 )
E)

Question 41

Biologists observed that as the temperature t (in degrees Fahrenheit) increased near a local ant colony the speed s that the ants traveled also increased. The data from this observation is shown in the table below. Find the linear regression equation based on the data provided to determine how fast the ants will walk with the temperature is 105 ºF. (Rounded to the nearest hundredth)

A) 3.74 cm/sec
B) 1.28 cm/sec
C) 80.67 cm/sec
D) 5.86 cm/sec
E) 1.15 cm/sec

Question 42

Casey and Mark are running a race at constant speeds. The graph below shows the distance d (in miles) they have traveled since they started the race at time t (in minutes). Which one of the following statements is true?

A) Not enough information
B) Mark is running faster than Casey.
C) Casey is running at 0.23 mph while Mark is running at 0.31 mph.
D) Casey is running at 4.3 mph while Mark is running at 3.2 mph.
E) Casey and Mark are both traveling at the same constant speed.

Question 43

Judy is making fruit punch by mixing water with fruit juice crystals. In order for the fruit punch to taste fruity Judy mixes 2.5 cups of fruit juice crystals with 11 cups of water. The number of cups of water w is proportional to the number of cups of fruit juice crystals c . If Judy has 40 cups of water how many cups of fruit juice crystals should she mix with the water? (Rounded to the nearest tenth)

A) 9.1 cups
B) 0.7 cups
C) 3.6 cups
D) 176 cups
E) 1.5 cups

Question 44

The following table shows the values of the number of gallons of water used by a family during the month of July. Find the linear regression equation based on the data provided to determine the number of gallons of water used on day 10. (Rounded to the nearest hundredth)

A) 12.50 gallons
B) 7.13 gallons
C) 13.66 gallons
D) 8.50 gallons
E) 11.01 gallons

Question 45

Find an equation for the line passing through the point that is parallel to the line passing through and .

A) y = 9 x
B) y = 9 x
C) y = x
D) y = x
E) y = x

Question 46

The cost for a cell phone plan at Store A starts at $26.99 per month plus $0.04 per minute. The cost for a cell phone plan at Store B starts at $36.99 per month plus $0.02 per minute. Determine the number of cell phone minutes used for which the monthly cost is the same at both Store A and Store B.

A) 500 minutes
B) 1066 minutes
C) 0 minutes
D) 167 minutes
E) 3199 minutes

Question 47

The following table shows the swim times s for a certain swimmer for the 400-meter freestyle swims during the years 2001 to 2007. Let represent the year 2001. Which one of the following equations is the line of best fit for the data provided? (Rounded to the nearest ten-thousandths)

A)
B)
C)
D)
E)

Question 48

A hotel finds that if it spends no money on renovations they will be able to rent 145 rooms per night. However they have found that for every $3500 spent on renovations they will be able to rent an additional 25 rooms per night. Let x represent the amount of money spent on renovations and y represent the number of rooms rented. How much money will need to be spent on renovations in order to rent 400 rooms per night?

A) $87500
B) $1400000
C) $76300
D) $35700
E) $56000

Question 49

Find an equation for the line passing through the point that is perpendicular to the line passing through and .

A) y = x
B) y = x
C) y = x
D) y = x
E) y = 5 x

Question 50

Which one of the following equations expresses the statement m is directly proportional to p ?

A)
B)
C)
D)
E)

Question 51

Find an equation for the line that is perpendicular to and passes through .

A) y = x
B) y = x
C) y = x
D) y = 2 x
E) y = -2 +2 x

Question 52

c is directly proportional to r . If then . Find the constant of proportionality. (Rounded to the nearest hundredth)

A)
B)
C)
D)
E)

Question 53

The following table shows the values of airfare for a roundtrip ticket from San Antonio TX to Portland OR. Which one of the following is the equation for a line of best fit for the data provided? (Rounded to the nearest tenth)

A)
B)
C) None of the above
D)
E)

Question 54

Find an equation for the line that is parallel to and passes through .

A) y = 26 3 x
B) y = 22 + 3 x
C) y = 7 x
D) y = x
E) y = 7 + 3 x

Question 55

A hotel finds that if it spends no money on renovations they will be able to rent 135 rooms per night. However they have found that for every $4000 spent on renovations they will be able to rent an additional 30 rooms per night. Let x represent the amount of money spent on renovations and y represent the number of rooms rented. Determine a model for the number of rooms rented as a function of the amount of money spent on renovations.

A) y = 135 + 30 x
B) y = 135 + x
C) y = 135 + x
D) y = 135 + x
E) y = 135 + 4000 x

Question 56

A swimming pool is being filled with water. The linear equation models the number of gallons w of water in the pool at time t (in minutes). If the pool has a capacity of 19500 gallons how long will it take for the pool to fill to capacity? (Rounded to the nearest tenth)

A) 3341.7 minutes
B) 3158.3 minutes
C) 3250.0 minutes
D) 18950.0 minutes
E) 91.7 minutes

Question 57

Which one of the following is the slope of a line that is perpendicular to the line shown in the graph below?

A) 0.91
B) -0.91
C) 1.1
D) -1.1
E) None of the above

Question 58

m is directly proportional to n . If is the constant of proportionality then find n when . (Rounded to the nearest hundredth)

A)
B)
C)
D)
E)

Question 59

Which one of the following equations has a graph that is parallel to the line shown in the graph below?

A)
B) None of the above
C)
D)
E)

Question 60

Biologists observed that as the temperature t (in degrees Fahrenheit) increased near a local ant colony the speed s that the ants traveled also increased. The data from this observation is shown in the table below. Determine the linear regression equation based on the data provided. (Rounded to the nearest thousandth)

A)
B)
C)
D)
E)

Question 61

Find the value of x that satisfies the equation when . (Rounded to the nearest hundredth)

A) 285.00
B) -55.00
C) 11.00
D) 2.38
E) 3.00

Question 62

For the equation the solution is .

Question 63

An economist models the market for rice by the following equations. Let p represent the price per bushel (in dollars) and y represent the number of bushels produced and sold (in millions). Use the model for supply to determine at what point is the price so low that no rice is produced.

A) When the price of rice is $141.85 per bushel.
B) When the price of rice is $70.93 per bushel.
C) When the price of rice is $5.46 per bushel.
D) When the price of rice is $12.99 per bushel.
E) When the price of rice is $2.38 per bushel.

Question 64

Find the value of x that satisfies the equation when .

A) 23
B)
C) 33
D)
E) -78

Question 65

An economist models the market for rice by the following equations. Let p represent the price per bushel (in dollars) and y represent the number of bushels produced and sold (in millions). Find the best approximation for the equilibrium price.

A) The equilibrium price is $1.23 per bushel.
B) The equilibrium price is $5.86 per bushel.
C) The equilibrium price is $3.97 per bushel.
D) The equilibrium price is $154.21 per bushel.
E) The equilibrium price is $2.58 per bushel.

Question 66

A quantity Q is related to quantity R by the equation . Find the value of Q when .

A) 10
B)
C)
D)
E)

Question 67

For the equation the solution is .

Question 68

A printing company determines that to print a large format poster it costs $75 to set up the production process. Each poster that is printed costs $25 in material and labor. The printing company sells these posters to marketing firms for $58 each. Determine the number of posters the printing company must sell to break even. [Note: profit = revenue - cost]

A) 75 posters
B) 0 posters
C) 3 posters
D) 2 posters
E) 33 posters

Question 69

The Subtraction Property of Equality states that when the same real number or algebraic expression is subtracted from both sides of an equation the solution is unchanged.

Question 70

Is an expression or an equation ?

A) expression
B) equation

Question 71

Using the graph below determine the point where the graphs intersect.

A)
B)
C)
D)
E)

Question 72

The cost of college tuition for 12 credit hours at two local colleges during 2003 to 2008 is shown in the table below. Determine the model for the cost of Tuition in School B as a function of the number of years since 2003.

A) B(t) = 31 + 291 t
B)
C) B(t) = 291 + 31 t
D) B(t) = 31 t
E)

Question 73

For the equation where T is the total tuition paid and c is the number of credits taken a solution is and .

Question 74

A printing company determines that to print a large format poster it costs $75 to set up the production process. Each poster that is printed costs $22 in material and labor. The printing company sells these posters to marketing firms for $60 each. Find a linear function P that models the profit from selling x posters. Note: profit = revenue - cost

A)
B)
C)
D)
E)

Question 75

Is an expression or an equation ?

A) expression
B) equation

Question 76

For the equation where D is the distance traveled in miles when you have been driving for t hours a solution is and .

Question 77

A speed camera records the distance that a car travels along a straight road by taking snapshots of the traveling car at two different times. The first snapshot shows the car is 36 ft away from the speed camera. After half a second the second snapshot shows the car is 8 ft away from the speed camera. Assume that the car is traveling at a constant speed.
a. Based on the speed camera evidence how fast is the car traveling?
b. Find a linear equation that models the car's distance y traveled for any amount of time x .
c. How many seconds after the first snapshot does it take for the car to reach the speed camera?
d. How far away from the speed camera was the car 1.5 seconds before the first snapshot was taken?

Question 78

The cost of college tuition for 12 credit hours at two local colleges during 2003 to 2008 is shown in the table below. Determine the year that the cost of tuition at School A is expected to be less than the cost of tuition at School B?

A) By 2010
B) By 2017
C) By 2013
D) By 2016
E) By 2009

Question 79

Find the point at which the graphs of the two linear equations intersect.

A) (0 0)
B) ( 5 )
C) ( )
D) ( )
E) ( )

Question 80

An economist models the market for rice by the following equations. Let p represent the price per bushel (in dollars) and y represent the number of bushels produced and sold (in millions). Use the model for demand to determine at what point is the price so high that no rice is sold.

A) When the price of rice is $8.42 per bushel.
B) When the price of rice is $0.32 per bushel.
C) When the price of rice is $221.58 per bushel.
D) When the price of rice is $0.04 per bushel.
E) When the price of rice is $5.32 per bushel.