To interpret the slope of the graph, we need to understand how the height of the hot air balloon changes over time.
Looking at the graph descriptions you've provided:
- The height is given in hundreds of feet (the vertical axis labels are 2, 4, 6, ..., which suggests heights of 200, 400, 600 feet, etc.).
- The time is given in minutes (the horizontal axis shows increments of 0, 4, 8, 12, etc.).
If the slope indicates the rate of ascent of the hot air balloon, we can calculate it from the increments of time and height:
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If the graph shows that the balloon rises 400 feet (which would be 4 on the vertical axis, as it represents 400 feet for every 100) over a time interval of 4 minutes, then the slope would be calculated as follows:
\[\text{Slope} = \frac{\text{Change in height}}{\text{Change in time}} = \frac{400 \text{ feet}}{4 \text{ minutes}} = 100 \text{ feet per minute}.\]
Thus, considering the options you provided:
- For every 2 minutes, the balloon rises 400 feet. (This implies a rise of 200 feet per minute, not correct)
- For every four minutes that pass, the balloon rises 200 feet. (This implies a rise of 50 feet per minute, not correct)
- The balloon will be at 200 feet when it is launched. (Not necessarily correct unless stated in the graph)
- For every four minutes that pass, the balloon rises 400 feet. (This is correct and implies a rise 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.