Answer:
The slope of a position-time graph can be calculated as:
[tex]m=\frac{\Delta y}{\Delta x}[/tex]
where
[tex]\Delta y[/tex] is the increment in the y-variable
[tex]\Delta x[/tex] is the increment in the x-variable
We can verify that the slope of this graph is actually equal to the velocity. In fact:
[tex]\Delta y[/tex] corresponds to the change in position, so it is the displacement, [tex]\Delta s[/tex]
[tex]\Delta x[/tex] corresponds to the change in time [tex]\Delta t[/tex], so the time interval
Therefore the slope of the graph is equal to
[tex]m=\frac{\Delta s}{\Delta t}[/tex]
which corresponds to the definition of velocity.
