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A graph of the function y=80x+2

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

direction traveled
direction traveled

speed traveled
speed traveled

miles 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 takes 0 minutes to descend 600 feet.
The balloon takes 0 minutes to descend 600 feet.

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

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

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

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

(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

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 400 feet.
For every four minutes that pass, the balloon rises 400 feet.

For every four minutes that pass, the balloon rises 200 feet.
For every four minutes that pass, the balloon rises 200 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 2 minutes, the balloon rises 400 feet.
For every 2 minutes, the balloon rises 400 feet.
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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=1,050−1,2259−8
m equals Start Fraction 1,050 minus 1,225 over 9 minus 8 End Fraction

m=525−70011−12
m equals Start Fraction 525 minus 700 over 11 minus 12 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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1 answer

Let's address each of the questions one by one:

  1. Question about Carli's road trip:

    • The x-axis represents time in hours. This is the only appropriate quantity for the x-axis based on the context of a road trip and the linear equation provided (y = 80x + 2), where 'x' symbolizes time, likely in hours.

  2. Question about the hot air balloon graph:

    • The y-intercept tells us that the balloon starts its descent at 600 feet. The y-intercept in this context represents the initial height of the balloon when the time (x) is zero.

  3. Question about the rental truck company's cost function:

    • The points that would appear on the linear function \( C = 1.25m + 25 \) are (2, 28.5) and (4, 31) when calculated for specific values of m (miles driven). However, given the response choices you provided, it seems like the choice should likely represent the situation described. If we work through the cost:
      • For \( m = 2 \): \( C = 1.25(2) + 25 = 2.5 + 25 = 27.5 \) (not matching the options provided).
      • For \( m = 4 \): \( C = 1.25(4) + 25 = 5 + 25 = 30 \) (not matching the options provided).
      • There might be an inconsistency in what points can be produced with a direct linear function, as all pairs \( (m, C) \) should hold.

  4. Question about the hot air balloon climbing graph:

    • The slope interpretation states for every four minutes that pass, the balloon rises 200 feet. To remain consistent and based on given options, it's crucial to derive if the unit changes indicate a calculated ratio in that direction.

  5. Question about Barton's car loan:

    • The correct slope formula representation from the choices given would be m = 2,450 - 2,625 / 0 - 1. Here, m represents the drop in the balance related to payments over the passage of months corresponding to his payment system. This is the typical way to illustrate how loan balances decrease over time with consistent payments.

For clarity, ensure understanding of each statement through careful interpretation of functions and correctly applied mathematical principles.