Entertainment Cable Company charges a monthly access fee plus an additional fee for each premium channel to which a customer subscribes. The graph below represents the current relationship.
The company has proposed to increase the amount charged for each premium channel by $1.50 per channel. Which equation shows the new monthly cost, c, where p is the number of premium channels to which a customer subscribes?
A. c = 30 + 4p
Incorrect. This equation represents the current pricing plan, which is the equation of the line shown in the graph.
B. c = 31.50 + 4p
Incorrect. This equation shows an increase of $1.50 in the y-intercept, or the monthly access fee.
C. c = 30 + 5.50p
Correct!
D. c = 31.50 + 5.50p
Incorrect. This equation shows both an increase in the y-intercept, which is the monthly access fee, and the slope, which is the amount charged for each premium channel.
Mike owns a plumbing company. He charges an hourly rate plus a charge for the service call. The table below shows the relationship between h, the number of hours of labor, and c, the total cost of Mike’s plumbing services.
If Mike decides to keep his service call charge the same, but increases his hourly rate by $2, what will the new total cost of a service call be that took 8 hours?
A. $180
Incorrect. This amount represents what Mike would charge if he doubled what he currently charges for a service call that took 4 hours.
B. $141
Incorrect. This amount represents what Mike would charge for a service call that took 8 hours if he did not change his hourly rate.
C. $143
Incorrect. This amount represents what Mike would charge if he increased the service call charge by $2.
D. $157
Correct!
Pedro visited his cousin in Amarillo, Texas. When he arrived, there were 5 inches of snow on the ground. The next day, snow started falling at a rate of 2 inches per hour. The graph below shows the amount of snow on the ground as the snow fell.
Which graph best represents the total depth of snow on the ground if it had snowed at a rate of 3 inches per hour?
A.
Incorrect. This graph shows a snowfall rate of 3 inches per hour, but neglects to show the 5 inches of snow that were already on the ground.
B.
Correct!
C.
Incorrect. The rate of 3 inches per hour should be shown on the graph as an increase in the vertical direction of 3 for each increase in the horizontal direction of 1.
D.
Incorrect. This graph shows the same rate of snowfall, 2 inches per hour, but with a starting point of 3 inches on the ground instead of 5 inches.
Autumn started 15 blocks from her house and began walking toward her house at a rate of 2 blocks per minute. The graph below shows the relationship between the time she walks and the number of blocks she is from her house.
How would the graph change if Autumn started 15 blocks from her house but walked at a rate of 3 blocks per minute?
A. The y-intercept would shift up 1 unit.
Incorrect. Autumn is still starting 15 blocks from home.
B. The steepness would remain the same.
Incorrect. The steepness changes when the rate changes.
C. The steepness would increase.
Correct! Since Autumn is walking faster, the line would be steeper.
D. The steepness would decrease.
Incorrect. Autumn is walking at a faster rate now.
Andrea purchased a new car. She borrowed $6,000 and makes monthly payments of $350. Which of the following linear functions could represent her remaining loan balance, b, if she increases her monthly payments by $75? Let m represent the number of months since Andrea purchased the car.
A. I only
Incorrect. Increasing the monthly payments by $75 changes the slope by 75 additional dollars per month.
B. I and II only
Incorrect. Function I shows a slope of 75, which is not what the slope of the new function would be.
C. II and III only
Incorrect. Function III shows the graph of the initial function, b = 6,000 – 350m.
D. II only
Correct!