The Slope of The Secant Line, The Average Rate of Change

So you know the slope. Now let's say that we have some function, whatever it is.
Let's assume this function passes through two whatever points.

We can pick these two points, and find the equation for a line that passes through them.
This line will have a slope.

Remember that a slope in mathematical context says "for every change in x, y changes by this much"!

The slope of such line passing through these two points is, in a sense, the average rate of change of this function along these two points.

This says that this m represents how much of a change in y we've had for a distance we've travelled along the x-axis.

You'll see where this all starts to come together now:
The Slope of The Secant Line Over an Infinitesimally Small Distance

Interactive Graph