The graph below displays the time in which it takes Runner A and Runner B to run 3 miles. Which statement correctly interprets the slope of the data displayed?
Runner B is a faster runner because the slope of the data is 6.
In the context of the graph, the slope represents the speed at which each runner completes 3 miles. The lower the slope, the faster the runner, as they take less time to run the same distance. Therefore, a slope of 6 for Runner B indicates that they are faster than Runner A.
This statement is incorrect because the slope of 6 corresponds to Runner B, not Runner A. Additionally, the lower slope indicates a faster speed, so even if the slope of 6 did correspond to Runner A, this would make Runner A the faster runner, not the slower.
This statement is also incorrect. Even if the slope for Runner A were 7, this would mean that Runner A is slower than Runner B, whose slope is 6. A higher slope indicates a slower speed, as it takes more time to run the same distance.
This statement is incorrect because the slope for Runner B is actually 6, not 7. Moreover, if Runner B's slope were 7, this would make him slower, not faster, as a higher slope indicates a longer time to run the same distance.
The slope of a graph in this context represents speed. The lower the slope, the faster the runner. Therefore, with a slope of 6, Runner B is the faster runner. Misinterpretations of the graph's slope as it pertains to each runner's speed led to the incorrect conclusions in options A, B, and D.
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