To interpret the slope of a graph representing the ascent of a hot air balloon, we need to understand how the changes in the x-axis (time in minutes) correlate to changes in the y-axis (height in feet).
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Understanding the Slope: The slope of the line in the graph indicates the rate of change of height with respect to time. If the slope is constant as described, it means the balloon is ascending at a steady rate.
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Analyzing the Options:
- "For every four minutes that pass, the balloon rises 400 feet." - This indicates a slope of \( \frac{400 \text{ feet}}{4 \text{ minutes}} = 100 \text{ feet per minute} \).
- "For every 2 minutes, the balloon rises 400 feet." - This indicates a slope of \( \frac{400 \text{ feet}}{2 \text{ minutes}} = 200 \text{ feet per minute} \).
- "The balloon will be at 200 feet when it is launched." - This is not an interpretation of the slope but rather an initial condition.
- "For every four minutes that pass, the balloon rises 200 feet." - This indicates a slope of \( \frac{200 \text{ feet}}{4 \text{ minutes}} = 50 \text{ feet per minute} \).
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Conclusion: Depending on the graph's specific steepness or lack thereof, the correct interpretation could vary. Without the actual graph, one can't definitively choose an answer, but if I were to guess based on common interpretations of ascent, the first option "For every four minutes that pass, the balloon rises 400 feet." would be a logical choice indicating a consistent and relatively steep ascent.
Choose the response that accurately reflects the slope shown in the graph based on your observation of it.
1 answer