To determine which object would reach 100 feet in the least amount of time, we need to find the slope of each line and compare them.
Line A passes through the points (0, 0) and (3, 6). The change in y is 6 - 0 = 6, and the change in x is 3 - 0 = 3. Therefore, the slope of line A is 6/3 = 2.
Line B passes through the points (0, 0) and (6, 6). The change in y is 6 - 0 = 6, and the change in x is 6 - 0 = 6. Therefore, the slope of line B is 6/6 = 1.
Line C passes through the points (0, 0) and (6, 3). The change in y is 3 - 0 = 3, and the change in x is 6 - 0 = 6. Therefore, the slope of line C is 3/6 = 1/2.
The slope represents the rate of change, or how quickly the distance increases with time. A larger slope indicates a steeper increase in distance over time.
Comparing the slopes, we find that line A has a slope of 2, line B has a slope of 1, and line C has a slope of 1/2.
Since line A has the largest slope, it indicates the fastest rate of increase in distance over time. Therefore, line A would reach 100 feet in the least amount of time compared to lines B and C.