Let's take the function y=x^2 as an example. Suppose you want to find the slope (that is, the rise divided by the run or, to be mathy, m=(y2-y1)/(x2-x1)) at the point x=1. Since y=x^2, y=1 so that we have the fixed point (1,1). Now, we need a second point to compute rise/run. Choose, say, x=4, y=16. Since you now have two points, you can compute the slope. Unfortunately, your line goes through two points. This is called a secant line, and is not a tangent line through the single point (1,1). Now, let's try it again with x=3, y=9. But, that's still a secant line, not a tangent line. Let's try again with x=2, y=4. Again, secant line, not tangent. But, notice that as we move from x=4 to x=3 to x=2, we are approaching x=1, our fixed point. The power rule for x^2 is 2x and gives you the slope at x=1 exactly and is the slope of the line tangent to x=1,y=1. It's not the slope of the secant line since it now involves only a single point.