How to calculate the slope of position time graph?

The slope of a position-time graph can be calculated as:

where

is the increment in the y-variable

is the increment in the x-variable

We can verify that the slope of this graph is actually equal to the velocity. In fact:

corresponds to the change in position, so it is the displacement,

corresponds to the change in time , so the time interval

Therefore the slope of the graph is equal to

which corresponds to the definition of velocity.