Linear Functions from Situations Quick Check

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

To interpret the slope of the graph of the hot air balloon's ascent, we need to understand that the slope represents the rate of change in height per unit of time.

The provided options are:

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

Without the specific details of the graph, I cannot give you the exact answer, but you should look for the change in height and the change in time represented by the graph to determine which option is correct.

  • If the slope indicates that for every 2 minutes the height increases by 400 feet, then the first option is correct.
  • If it indicates that for every 4 minutes the height increases by 400 feet, then choose the second option.
  • If it indicates an increase of 200 feet over 4 minutes, select the third option.
  • The fourth option regarding the initial height at launch indicates a y-intercept value.

Usually, the slope interpretation will depend on how much the height increases for a given time interval as indicated on the graph. Look for these numerical values on the graph to choose the correct response.

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