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distance time graph is a graph traveled in a graph which shows how much we have traveled in equal period of time.
The slope of a distance-time graph represents speed.
Typically distance is plotted on the y-axis of a distance-time graph.
speed is the gradient under the distance vs time graph which is change in distance /change in time
As the body is at rest, its distance from some point is not changing, so the graph will be a straight line parallel to the time axis (including the possibility of being on the time axis).