Points and Lines

Suppose there are at least two points on the plane, and not all of them lie on a single straight line. Prove that there exist a line that passes through exactly two of the points.

Comment

This is the Sylvester–Gallai theorem There is a proof in Proofs from THE BOOK . A great explanation can also be found in this Ebima Lab’ YouTube video (in Japanese but English subtitles are available). I think that this Cirno in this video is too smart…