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The answer will depend on whether the graph is a distance time graph or a speed time graph.
The slope of a distance-time graph shows that speed of the object in the direction towards or away from the point of reference (usually the origin). It indicates absolutely nothing about its speed in any other direction. So, for example, an object could be rotating around the origin at the speed of light (the fastest possible) and the distance-time graph would show it being stationary bacause its distance from the origin is not changing!
The slope of the speed-time graph indicated the acceleration of the object, again with the same qualification.
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What does the slope of a speed vs time graph indicate an object's motion?
The slope of a speed vs time graph indicates an objects acceleration.
What does the slope of a distance vs time graph indicate about an object's motion?
instantaneous velocity
What does a horizontal slope of a distance versus time graph indicate about an objects motion?
It is a measure of speed of the object, but only in the radial direction: that is, towards or away from the point from which distance is measured. The object could be going around that point in circular motion and the graph would show absolutely nothing.
What does the slope of a distanced-time graph indicate?
magnitude of velocity
What information can you get from looking at the slope of a motion graph?
The rate of acceleration.
