What does the slope of a distance-versus-time graph represent?
The slope of a position-versus-time graph represents the velocity.
The slope of the tangent line represents the rate of change of a function. Velocity is the rate of change of position with respect to time. Equivalently, velocity is the derivative of the position function.
The average velocity has limited usefulness for an object whose velocity is not constant.
We can define an object's instantaneous velocity at a single instant of time,