In a distance-time graph, how is speed represented?

In a distance-time graph, speed is represented by the slope of the graph. The slope measures how much distance is covered over a period of time; therefore, it can indicate how fast an object is moving. A steeper slope signifies a higher speed, as the object covers a larger distance in the same amount of time, while a gentle slope indicates a slower speed.

To understand this better, consider how slope is calculated: it is the change in distance (vertical axis) divided by the change in time (horizontal axis). This ratio directly correlates to speed, demonstrating that the steeper the slope, the greater the speed.

In contrast, the area under a distance-time graph does not quantify speed; it would rather represent total distance traveled over an interval. The y-intercept indicates the starting distance at time zero but does not give information about speed. The x-intercept relates to the time when distance is zero, which does not inform about speed either. Therefore, the best representation of speed on a distance-time graph is indeed the slope of the graph.