Question 1

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

Accepted Answer

The two slopes are different, so the graphs are not perpendicular. In fact, the slopes must have opposite signs and be reciprocals of each other for the graphs to be perpendicular.

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

Accepted Answer

D

Question 3

The slope of the function  is  .

Accepted Answer

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.

Accepted Answer

The cost includes a fixed initiation fee, so it is not directly proportional to the number of months.

Question 5

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

Accepted Answer

The answer of If the slope of a line is...

Question 6

Which one of the following graphs illustrates the equation y = 4   x ?
A) 
B) 
C) None of these options
D) 
E)

Accepted Answer

The equation y = 4x has a slope of 4, which means for every 1 unit increase in x, there is a 4 unit increase in y. Only graph D has a slope of 4, so it is the correct choice.

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

Accepted Answer

The answer of After taking a bath you begin to...

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

Accepted Answer

The answer of Find the equation of a line that...

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.

Accepted Answer

This statement is true because any increase or decrease in the number of gallons of gas purchased will directly affect the cost of filling a car's tank, which is proportional to the price per gallon.

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)

Accepted Answer

The answer of The owner of a gas station records...

Question 11

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

Accepted Answer

The answer of The graph of the line  and...

Question 12

Find the equation of the line for the following graph. 
A) 
B) 
C) 
D) 5
E)

Accepted Answer

The answer of Find the equation of the line for...

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

Accepted Answer

The answer of Find the slope and y -intercept for...

Question 14

Find the equation of a line with slope = -8 and y -intercept of 2.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the equation of a line with...

Question 15

Which one of the following graphs illustrates the equation  ?
A) 
B) 
C) 
D) None of these options
E)

Accepted Answer

The answer of Which one of the following graphs illustrates...

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)

Accepted Answer

The answer of After taking a bath you begin to...

Question 17

Given the graph below find the rise over run between any two points. 
A) -3
B) 2
C) 3
D) 
E)

Accepted Answer

The answer of Given the graph below find the rise...

Question 18

The y -intercept of the function  is  .

Accepted Answer

The answer of The y -intercept of the function ...

Question 19

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

Accepted Answer

The slope of a line cannot be expressed in that format. Without knowing the actual value of the slope, we cannot determine the change in the run.

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

Accepted Answer

The relationship is linear, so we can use the two points (1.77, 1000) and (2.32, 400) to find the equation of the line. The slope is (400 - 1000) / (2.32 - 1.77) = -600 / 0.55 = -1090.91. Using point-slope form, y - 1000 = -1090.91(x - 1.77). Solving for y when x = 2.19 gives approximately 542 gallons.

Quiz 2: Linear Equations and Inequalities With One Variable

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

The slope-intercept form of the equation is:

The slope of the function is .

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.

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

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

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?

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

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.

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

Find the equation of the line for the following graph.

Find the slope and y -intercept for the equation .

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

Which one of the following graphs illustrates the equation ?

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

The y -intercept of the function is .

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