A position-time graph plots signed position on the vertical axis against time on the horizontal axis.
The ordinate gives the object's position at an instant. The gradient gives velocity: a positive gradient means motion in the positive direction, a negative gradient means motion in the negative direction, and a horizontal tangent means zero instantaneous velocity.
Changing gradient means changing velocity. A curve that becomes progressively steeper has increasing speed; the sign of the curvature indicates the sign of acceleration only after the chosen axis and the velocity trend are interpreted carefully.
The gradient of a chord gives average velocity over a finite interval,
The gradient of a tangent estimates instantaneous velocity at one time. A straight line has constant velocity; a curved line has changing velocity. The area under a position-time graph has no standard kinematics meaning.