A graph of the function y=80x+2

Question

models Carli’s road trip, with her speed measured in miles per hour. The graph includes the two hours of stops she’ll make. Using this information, define which quantity describes the x-axis.(1 point)
Responses

time in hours
time in hours

miles traveled
miles traveled

speed traveled
speed traveled

direction traveled
Use the image to answer the question.

A coordinate plane's x-axis ranges from 0 to 30 by 10-unit increments and its y-axis ranges from 0 to 600 by 200-unit increments. A diagonal line is plotted.

The graph models the descent of a hot air balloon in feet per minute. What does the y-intercept tell you in this situation?

(1 point)
Responses

The balloon rises 600 feet.
The balloon rises 600 feet.

The balloon starts its descent at 600 feet.
The balloon starts its descent at 600 feet.

It will take the balloon 600 minutes to descend.
It will take the balloon 600 minutes to descend.

The balloon takes 0 minutes to descend 600 feet.
The balloon takes 0 minutes to descend 600 feet.
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Question
A rental truck company charges $25 to rent a truck, then $1.25 for every mile it is driven. The situation can be expressed as C=1.25m+25
, where C
is the total cost to rent the truck and m is the miles driven. If you plot points on the linear function, which of the following would appear?(1 point)
Responses

(4,30)
and (8,35)
left parenthesis 4 comma 30 right parenthesis and left parenthesis 8 comma 35 right parenthesis

(2,22.5)
and (4,20)
left parenthesis 2,22.5 right parenthesis and left parenthesis 4 comma 20 right parenthesis

(2,2.5)
and (4,5)
left parenthesis 2 comma 2.5 right parenthesis and left parenthesis 4 comma 5 right parenthesis

(30,4)
and (35,8)
left parenthesis 30 comma 4 right parenthesis and left parenthesis 35 comma 8 right parenthesis
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Question
Use the image to answer the question.

A line with an arrow at the top is plotted in quadrant 1 of a coordinate plane. The x-axis is labeled Time in Minutes, and the y-axis is labeled Height in feet left parenthesis per hundred right parenthesis.

A hot air balloon climbs into the air at a steady rate per minute. The graph illustrates the hot air balloon’s ascent. Interpret the slope of the graph.

(1 point)
Responses

For every four minutes that pass, the balloon rises 200 feet.
For every four minutes that pass, the balloon rises 200 feet.

For every 2 minutes, the balloon rises 400 feet.
For every 2 minutes, the balloon rises 400 feet.

The balloon will be at 200 feet when it is launched.
The balloon will be at 200 feet when it is launched.

For every four minutes that pass, the balloon rises 400 feet.
For every four minutes that pass, the balloon rises 400 feet.
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Question
Use the image to answer the question.

A line with an arrow at the bottom is plotted in quadrant 1 of a coordinate plane. The x-axis is labeled Months, and the y-axis is labeled Amount in Dollars.

Barton took out a car loan of $2,625. He makes monthly payments of $175. The graph represents the remaining balance after each payment. Which example models the correct slope?

(1 point)
Responses

m=525−70011−12
m equals Start Fraction 525 minus 700 over 11 minus 12 End Fraction

m=1,050−1,2259−8
m equals Start Fraction 1,050 minus 1,225 over 9 minus 8 End Fraction

m=9−81,050−1,225
m equals Start Fraction 9 minus 8 over 1,050 minus 1,225 End Fraction

m=2,450−2,6250−1
m equals Start Fraction 2,450 minus 2,625 over 0 minus 1 End Fraction
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Answer 1

Let's go through each question one by one.

Question 1

What quantity describes the x-axis in the function \(y=80x+2\)?

The equation illustrates Carli’s road trip, where \(y\) represents the speed in miles per hour, and \(x\) indicates the time. With two hours of stops included, the \(x\)-axis would represent:

• Time in hours (Correct Response)

Question 2

What does the y-intercept tell you in the context of the hot air balloon descent?

The y-intercept represents the initial height from which the balloon descends. Therefore, the correct interpretation is:

• The balloon starts its descent at 600 feet. (Correct Response)

Question 3

Using the equation \(C = 1.25m + 25\), which coordinates would appear?

To find points, we can substitute values for \(m\) into the equation.

• For \(m = 2\): \[ C = 1.25(2) + 25 = 2.5 + 25 = 27.5 \] So the point is (2, 27.5).

• For \(m = 4\): \[ C = 1.25(4) + 25 = 5 + 25 = 30 \] So the point is (4, 30).

No combinations match (2, 27.5), so let's check the other options:

• For \(m = 8\): \[ C = 1.25(8) + 25 = 10 + 25 = 35 \] So this produces (8, 35).

Thus, the correct pair is:

• (4, 30) and (8, 35) (Correct Response)

Question 4

Interpret the slope of the hot air balloon ascent.

Suppose the slope is given as an increase in height per given time (e.g., feet per minute), if the statement says "For every four minutes that pass, the balloon rises 400 feet," it indicates how the balloon's height increases with time.

Thus, if the response states:

• For every four minutes that pass, the balloon rises 400 feet. (Correct Response)

Question 5

Which example models the correct slope for Barton’s car loan?

To find the slope of the graph, we need to calculate it as a ratio of the change in amount to the change in months:

1. From $2625 to $2450 in 1 month (after one payment of $175), \[ m = \frac{2450 - 2625}{0 - 1} = \frac{-175}{-1} = 175 \]

2. Other points can be checked similarly:

   • From (0, 2625) to (1, 2450).

However, we grep the option that samples the initial balance and payment correctly:

• m = \frac{2625 - 2450}{0 - 1} gives the slope indicating the change after the first payment.

Thus, if using the paired amounts at two payments:

• m = \frac{2,450 - 2,625}{0 - 1} correctly illustrates the loan decrease.
• This simplifies to m = -175 per month. (Correct Response)

Please review these responses, and let me know if you need anything else!