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.

Question

(1 point)
Responses

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

For every 2 minutes, the balloon rises 400 feet.

Answer 1

To determine the correct interpretation of the slope of the graph, we need to assess how the height of the balloon changes over time.

The slope of a graph representing the balloon's ascent is calculated as the change in height (rise) divided by the change in time (run).

If we see that the balloon rises 400 feet over a span of 4 minutes, we can calculate the slope as follows:

• Rise = 400 feet
• Run = 4 minutes

So, the slope (rate of ascent) is:

Slope = Rise / Run = 400 feet / 4 minutes = 100 feet per minute.

Looking at the given responses, we need to focus on how the balloon rises relative to time. The correct interpretation is:

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

This makes sense in explaining the balloon's constant rate of ascent depicted in the graph. Thus, that response is the best choice.