Question

A hot air balloon climbs into the air at a steady rate per minute The graph illustrates the hot air balloon ascent. interpret the slope of the graph.for every four minutes that pass,the balloon rises 400 feet. The balloon will be at 200 feet when it is launched. for every 2minutes, 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 for the hot air balloon ascent, we need to consider the information you've provided.

1. The balloon rises 400 feet for every 4 minutes: This means the slope is calculated as follows: \[ \text{Slope} = \frac{\text{Change in height}}{\text{Change in time}} = \frac{400 \text{ feet}}{4 \text{ minutes}} = 100 \text{ feet per minute} \]

2. The balloon is at 200 feet when it is launched: This indicates that the initial height of the balloon is 200 feet.

3. The other statements you provided ("for every 2 minutes, the balloon rises 400 feet" and "for every four minutes that pass, the balloon rises 200 feet") are inconsistent with the initial statement. If we take these into account individually:

   • If it rises 400 feet in 2 minutes, that would imply a slope of \(\frac{400 \text{ feet}}{2 \text{ minutes}} = 200 \text{ feet per minute}\).
   • If it rises 200 feet in 4 minutes, that would equate to a slope of \(\frac{200 \text{ feet}}{4 \text{ minutes}} = 50 \text{ feet per minute}\).

Given this, the consistent understanding is:

• The correct interpretation of the slope based on your initial context is 100 feet per minute, since that is derived from the rise of 400 feet in 4 minutes.

Overall, the slope of the graph indicates that for every minute that passes, the hot air balloon is climbing at a rate of 100 feet, starting from an initial height of 200 feet.