Question
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.
the start point is (0,0)
the end point is (24,1200)
(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 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.
For every four minutes that pass, the balloon rises 400 feet.
the start point is (0,0)
the end point is (24,1200)
(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 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.
For every four minutes that pass, the balloon rises 400 feet.
Answers
Answered by
GPT-4o mini
To determine the slope of the graph for the hot air balloon's ascent, we can analyze the coordinates given. The start point is (0, 0) and the endpoint is (24, 1200).
The slope (rate of ascent) can be calculated as:
\[
\text{slope} = \frac{\text{change in height}}{\text{change in time}} = \frac{1200 \text{ feet} - 0 \text{ feet}}{24 \text{ minutes} - 0 \text{ minutes}} = \frac{1200 \text{ feet}}{24 \text{ minutes}} = 50 \text{ feet per minute}
\]
Now we need to interpret the given options in relation to this slope.
1. **For every 2 minutes, the balloon rises 400 feet.**
- This implies a rate of 200 feet per minute (400 feet / 2 minutes), which is incorrect.
2. **For every four minutes that pass, the balloon rises 200 feet.**
- This implies a rate of 50 feet per minute (200 feet / 4 minutes), this matches our calculation of slope over a wider interval.
3. **The balloon will be at 200 feet when it is launched.**
- This is incorrect because it starts at 0 feet.
4. **For every four minutes that pass, the balloon rises 400 feet.**
- This implies a rate of 100 feet per minute (400 feet / 4 minutes), which is incorrect.
Therefore, the correct interpretation of the slope of the graph is:
**For every four minutes that pass, the balloon rises 200 feet.**
The slope (rate of ascent) can be calculated as:
\[
\text{slope} = \frac{\text{change in height}}{\text{change in time}} = \frac{1200 \text{ feet} - 0 \text{ feet}}{24 \text{ minutes} - 0 \text{ minutes}} = \frac{1200 \text{ feet}}{24 \text{ minutes}} = 50 \text{ feet per minute}
\]
Now we need to interpret the given options in relation to this slope.
1. **For every 2 minutes, the balloon rises 400 feet.**
- This implies a rate of 200 feet per minute (400 feet / 2 minutes), which is incorrect.
2. **For every four minutes that pass, the balloon rises 200 feet.**
- This implies a rate of 50 feet per minute (200 feet / 4 minutes), this matches our calculation of slope over a wider interval.
3. **The balloon will be at 200 feet when it is launched.**
- This is incorrect because it starts at 0 feet.
4. **For every four minutes that pass, the balloon rises 400 feet.**
- This implies a rate of 100 feet per minute (400 feet / 4 minutes), which is incorrect.
Therefore, the correct interpretation of the slope of the graph is:
**For every four minutes that pass, the balloon rises 200 feet.**