Hopefully this one makes sense:
The derivative's definition is lim h → (0f (x + h) −f (x)) / h .
Explain with one sentence what gives the fraction (f (x + h) −f (x)) / h and with another sentence what will be the difference when you add lim → 0?
actually, the derivative is
lim(h→0) (f(x+h)-f(x))/h
slope is ∆f/∆x, which is exactly the expression given above, if ∆x = h.
google can provide many discussions of this concept.