Use the image to answer the question.

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 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.

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

Answer 1

To interpret the slope of the graph, we need to understand the relationship it represents. The slope of a graph is calculated as the "rise" over the "run." In this case, the "rise" would represent the change in height (in feet) and the "run" would represent the change in time (in minutes).

Given the options provided, we need to look for the correct interpretation of the slope regarding the rate at which the hot air balloon rises per unit of time.

1. For every 2 minutes, the balloon rises 400 feet.
2. The balloon will be at 200 feet when it is launched.
3. For every four minutes that pass, the balloon rises 400 feet.
4. For every four minutes that pass, the balloon rises 200 feet.

If the balloon rises 400 feet for a specific amount of time, the corresponding time interval to rise this height should also match the given slope interpretation.

• If the balloon rises 400 feet in 2 minutes, the rate of ascent would be 200 feet per minute.
• If it rises 400 feet over 4 minutes, that would equal a rise of 100 feet per minute.

With these calculations in mind, the best interpretation of the slope will be contingent on the specific values shown on the graph (which we cannot see). However, if we assume a standard interpretation based on regular increments:

• The correct answer would likely be: "For every four minutes that pass, the balloon rises 400 feet," which suggests a consistent rate of ascent over a longer timeframe.

Without seeing the graph or having the exact slope values, it’s best to say the slope interpretation hints at a consistent rise relative to time. But based on general assumptions, it cannot be definitively stated without visual confirmation.

If the graph implies a rapid ascent, option 1 may also link if it correlates with the given data. Thus, knowing exact values on the graph is crucial for a precise answer.

Answer 2

so whats the answer

Answer 3

Without seeing the specific values on the graph, I can provide an educated guess based on common interpretations of slope in a scenario like this involving a hot air balloon ascending steadily.

If we assume that the graph shows a steady ascent of the hot air balloon, the most likely answer from the options you provided would be:

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

This indicates a consistent rate of ascent that would typically be represented in such a scenario. If the graph supports a different interpretation based on the specific rise and run values, please refer to that data to validate the conclusion.

Answer 4

Linear Functions from Situations Quick Check
5 of 55 of 5 Items

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=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

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

m=1,050−1,2259−8

Answer 5

To determine which example correctly models the slope of the graph representing Barton’s car loan payments, we need to understand the situation first.

Barton took out a car loan of $2,625 and makes monthly payments of $175. Therefore, the remaining balance on the loan decreases by $175 for each month that passes.

Understanding Slope: The slope \( m \) can be calculated using the formula:

\[ m = \frac{\text{change in y}}{\text{change in x}} = \frac{\text{change in Amount}}{\text{change in Months}} \]

In this case, the change in the amount (the balance remaining) is negative because the balance decreases as he makes payments. After one month, the balance will be:

\[ 2,625 - 175 = 2,450 \]

To find the appropriate slope representation from the options:

1. \( m = \frac{9 - 8}{1,050 - 1,225} \)
2. \( m = \frac{2,450 - 2,625}{0 - 1} \)
3. \( m = \frac{525 - 700}{11 - 12} \)
4. \( m = \frac{1,050 - 1,225}{9 - 8} \)

Let’s evaluate each option:

1. Option 1 does not relate to the amount or months relevant to the loan situation.

2. Option 2 calculates the slope for the first month correctly:

   • Change in Amount: \( 2,450 - 2,625 = -175 \)
   • Change in Months: \( 0 - 1 = -1 \)
   • This gives \( m = \frac{-175}{-1} = 175 \) (correct slope of monthly payments).

3. Option 3 is not relevant to the monthly payment situation.

4. Option 4 does not relate to the amounts in the car loan context.

Based on the function of the car loan, the correct choice is: \( m = \frac{2,450 - 2,625}{0 - 1} \)

This option accurately reflects the scenario where the loan balance decreases with each payment made.