The question is:

(a,b) and (c,d) are two distinct points in R^2. Prove there exists a unique line passing through them.

I proved that a line exists:

y=[(d-b)/(c-a)]x + [b-(d-b)a/(c-a)]

But how do I prove that it is unique? I know the technique, you say that there are two and prove that they are the same, but how do I go about it in this problem? Thank you for your help!