What does the slope of a Position vs. Time graph represent?

Your question asks what the slope of a Position vs. Time graph represents.

Your answer would be Velocity.

The slope of a Position vs. Time graph would represent the velocity of the object.

If the slope is positive, then the object has a positive velocity, in which it is going forward.

If the slope is negative, then the object has a negative velocity, which means that it's going the opposite direction, or backwards.

If the slope is at a "horizontal" position, this means that the object is stopped or isn't moving at all.