# Tangent to a a curve, something seems wrong (Calculus)

I'm studying Calculus and i can see that the definition of the tangent to a point on a curve is

y= f'(a)(x-a)+b this must mean that

f'(a) = (y-b)/(x-a)

But that to me seems troubeling, because f'(a) is the slope at ONE point, while (y-b)/(x-a) is a quotient with the differene between 2 points. Is there a better explanation?

HallsofIvy