What type of motion is occurring when the slope of a velocity vs. time graph is zero?

If the speed/time graph is horizontal, that means that the speed isn't changing. The object is moving at a constant speed.

The VELOCITY may not be constant, though. Velocity includes the direction of the motion which is almost impossible to show on a graph. For example, if an object is in uniform circular motion, then its speed is constant and its speed/time graph is flat. But its velocity is constantly changing because the direction of the circle keeps changing.