Prove that only one straight line passes through two point

[parshyaa]

I was just thinking of basic definitions of geometry and i came to this question, so how could i prove that only one straight line passes through two distinct points.

 

[mfb]

You have to require that in the axioms, otherwise you get non-euclidean geometry where multiple different lines can go through two points.

 

[mathman]

Simple example - non-Euclidean: sphere, where all longitude lines go through both poles.