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

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

Answer 1

To interpret the slope of the graph of a hot air balloon's ascent, we need to analyze the information provided about the balloon's rise.

The statement includes several options regarding the rise of the balloon:

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

   • This means the rate of ascent is \( \frac{400 \text{ feet}}{4 \text{ minutes}} = 100 \text{ feet per minute}\).

2. The balloon will be at 200 feet when it is launched.

   • This indicates the initial height of the balloon at the time of launch, which does not directly affect the slope but provides context for where the ascent starts.

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

   • This results in a rate of ascent of \( \frac{200 \text{ feet}}{4 \text{ minutes}} = 50 \text{ feet per minute}\).

4. For every 2 minutes, the balloon rises 400 feet.

   • The rate here is \( \frac{400 \text{ feet}}{2 \text{ minutes}} = 200 \text{ feet per minute}\).

To find the correct interpretation of the slope in the graph, we look at the option that specifies the consistent rate of ascent over time. If the given condition is that the balloon rises 400 feet in 4 minutes, the slope of the graph indicates that the balloon is ascending at a rate of 100 feet per minute.

Therefore, the correct interpretation of the slope of the graph is:

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