Derivative of a line

1. Nov 2, 2004

danne89

Hi again! Time for one more of my newbie questions.
I'm reading "Elementary Calculus: An Approach Using Infinitesimals
" http://www.math.wisc.edu/~keisler/calc.html and can't get a theorem on a lines derivative. It goes like this:
$$f(x)=kx+b \Rightarrow \frac{dy}{dx} = f'(x) = k$$

That doesn't make seens to me because the definition of a tangent line is
g(x)=f'(x)(x-a)+b, there (a, b) is the point of the tangent.

For instance, let's say f(x)=2x. The f'(x)=2, using the above theorem. And then the tangent for the point (2, 2) ought to be l(x)=2(x-2)+2=2x-4+2=2x-2. But it's parallell to f(x)=2x!! :surprised What am I doing wrong, please give me a hint!

2. Nov 2, 2004

arildno

Eeh, the point is (1,2), not (2,2), so:
l(x)=2(x-1)+2=2x

3. Nov 2, 2004

danne89

Ohh. I took a point OUTSIDE the line. I feel so dumb...

4. Nov 2, 2004

danne89

Thanks for the support. By the way, many from Scandinavia here, isn't. The reson to care is that I'm a Swede. Anyway, maybe enought OT talk now.