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 200 feet.
For every four minutes that pass, the balloon rises 200 feet.
For every four minutes that pass, the balloon rises 400 feet.
For every four minutes that pass, the balloon rises 400 feet.
The balloon will be at 200 feet when it is launched.
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 200 feet.
For every four minutes that pass, the balloon rises 200 feet.
For every four minutes that pass, the balloon rises 400 feet.
For every four minutes that pass, the balloon rises 400 feet.
The balloon will be at 200 feet when it is launched.
Answers
GPT-4o mini
To interpret the slope of the graph, we need to understand that the slope represents the rate of change of height with respect to time.
If we assume the slope is \( m \) (rise over run), it can be expressed as:
\[
m = \frac{\text{change in height}}{\text{change in time}} = \frac{\text{Height (in feet)}}{\text{Time (in minutes)}}
\]
In the options provided, the key parts of the interpretation relate to how height increases with time.
Assuming from your options:
- If the slope indicates that every 2 minutes the balloon rises 400 feet, this suggests a rise of 200 feet per minute.
- If it indicates that every 4 minutes the balloon rises either 200 feet or 400 feet, this suggests different rates of ascent.
Taking into account the possible accurate interpretations based on typical graph slopes:
If the slope is **steep**, it would indicate a fast increase in height (e.g., rising 400 feet every 4 minutes), whereas a **gentler slope** would show a slower increase (e.g., rising only 200 feet every 4 minutes).
Therefore, if the slope indicates a rise of 400 feet for every 4 minutes, it would correspond with a rate of 100 feet per minute, but if it indicates 200 feet for every 4 minutes, it would indicate a rise of 50 feet per minute.
Finally, without the specific values from the graph, the correct interpretation based on the provided responses would likely be:
**For every four minutes that pass, the balloon rises 400 feet.**
This assumes a consistent, positive slope reflecting steady ascent in height over time.
If we assume the slope is \( m \) (rise over run), it can be expressed as:
\[
m = \frac{\text{change in height}}{\text{change in time}} = \frac{\text{Height (in feet)}}{\text{Time (in minutes)}}
\]
In the options provided, the key parts of the interpretation relate to how height increases with time.
Assuming from your options:
- If the slope indicates that every 2 minutes the balloon rises 400 feet, this suggests a rise of 200 feet per minute.
- If it indicates that every 4 minutes the balloon rises either 200 feet or 400 feet, this suggests different rates of ascent.
Taking into account the possible accurate interpretations based on typical graph slopes:
If the slope is **steep**, it would indicate a fast increase in height (e.g., rising 400 feet every 4 minutes), whereas a **gentler slope** would show a slower increase (e.g., rising only 200 feet every 4 minutes).
Therefore, if the slope indicates a rise of 400 feet for every 4 minutes, it would correspond with a rate of 100 feet per minute, but if it indicates 200 feet for every 4 minutes, it would indicate a rise of 50 feet per minute.
Finally, without the specific values from the graph, the correct interpretation based on the provided responses would likely be:
**For every four minutes that pass, the balloon rises 400 feet.**
This assumes a consistent, positive slope reflecting steady ascent in height over time.