I have a question on my homework that I'm on a bit stumped on, I mean, I know how to use the difference quotient easy-breezy, but this really stumped me because it asks me WHY its a valid formula.

If anyone could help me out and point me in the right direction I'd really appreciate it!

Question:

The slope of the tangent to a curve y=f(x) at a point P(a,f(a)) is *insert difference quotient here as 'h' approaches zero*.

Using words and a diagram, explain the validity of the equation.