The Slope of The Secant Line Over an Infinitesimally Small Distance

As you go from x = 1, to x = 2, you have .
During this movement along the graph, you have moved from y = 1, to y = 4, so
The slope of the line at these two points will therefore be

Now, we know for sure that (x=1,y=1) must be a point on this line.

We now have our secant line along these points.

Now what happens if we take a smaller and smaller distance?

The Tangent Line