Let $K$ be a field. Prove that projective transformation of a projective line determined by an affine line $K$ is the same as homography.
This means that I need to prove that it has the form: $x \rightarrow \frac{ax+b}{cx+d}, \ \ a,b,c,d \in K, ad-bc \neq 0$.
I don't know how to approach this .
Could you help me?
Thank you.