You have a motion graph for an object that shows distance and time. how does the slope of the graph relate to the object's speed?

If you graph the distance an object has gone at several instants
of time, then the slope of the graph at any place on it IS the speed
of the object at that instant.

If the object holds a constant speed, then the distance/time graph
is a straight line, whose slope is equal to the speed.

If the object's speed is not constant, then the graph may have curves
in it.  Still, it has a slope at every point ... the slope of a ruler that you
might lay down on the curved line at that point ... and the slope is the
object's speed at that point in time.

If the object is standing still and not moving, then its distance doesn't
change as time goes on.  The distance graph is flat/horizontal as long
as the object stays where it is ... the slope of that part of the graph is
zero ... the object's speed again.

Answerwavelength;