You probably remember your teachers referring to the slope as the “rise” over the “run.” The rise is the
difference between the y-coordinates, and the run is the difference between the x-coordinates. The slope
is the ratio of the two.
Now for a few changes in notation. Instead of calling the x-coordinates x 1 and x 2 , we’re going to call them
x 1 and x 1 + h, where h is the difference between the two x-coordinates. Second, instead of using y 1 and y 2 ,
we use f(x 1 ) and f(x 1 + h). So now the graph looks like the following:
Sometimes, instead of h, some books use ∆x.