Final answer:
The slope at a specific point on a position by time graph represents the instantaneous velocity at that point. The slope of a tangent line drawn at the point on the curve provides this value, while a constant slope on a straight-line graph would signify average velocity.
Step-by-step explanation:
The slope at a specific time point on a position by time graph indicates the instantaneous velocity at that point. On such a graph, the slope at any given point can be found by drawing a tangent line to the curve at the point of interest and calculating the slope of this straight line. This is because the slope of a position versus time graph is equal to the change in displacement divided by the change in time, which is the definition of velocity.
For a straight-line graph of position versus time, the slope represents the average velocity since it is constant across the entire time interval. The case is different for curved graphs, which represent the changing velocity over time; here, the instantaneous velocity must be found by taking the slope of the tangent line at any specific point on the curve. Additionally, when analyzing a velocity versus time graph, the slope would represent the average or instantaneous acceleration, while the area under the curve would represent the displacement.