To interpret the slope of the graph effectively, we need to understand that the slope represents the rate of change in the vertical position (height) of the hot air balloon with respect to time.
If the provided statement indicates that "For every four minutes that pass, the balloon rises 400 feet," this means the slope of the graph would be 400 feet per 4 minutes, or 100 feet per minute.
If instead the statement was "For every four minutes that pass, the balloon rises 200 feet," the slope would be 200 feet per 4 minutes, or 50 feet per minute.
Based on the responses you provided, the correct interpretation of the slope can be identified as follows:
- For every four minutes that pass, the balloon rises 200 feet. (This implies a slope of 50 feet per minute)
- The balloon will be at 200 feet when it is launched. (This refers to the height at launch, not the slope)
- For every 2 minutes, the balloon rises 400 feet. (This implies a slope of 200 feet per minute)
- For every four minutes that pass, the balloon rises 400 feet. (This implies a slope of 100 feet per minute)
Hence, if the graph shows that for every 4 minutes the balloon rises 400 feet, then this option would reflect a positive and substantial rate of ascent, which can be described as steady.
Conclusion
The correct answer regarding the slope interpretation would be: For every four minutes that pass, the balloon rises 400 feet.