The area under a velocity-time graph gives the displacement. The velocity-time and acceleration-time graphs for common motions are shown below.

But if you calculate the acceleration without the graph, you are explicitly stating that the y-intercept is zero---which it might not be. So there are some actual reasons for making a graph.

Velocity-time graphs show how the velocity (or speed) of a moving object changes with time. These graphs also show if the object is moving at a constant speed or accelerating, decelerating, or still.