The Slope Problem

Given 3 or more non-collinear points on a plane how many distinct slopes to these points define on the plane? We will prove the following theorem.

Theorem: If n>2 points in the plane do not lie on one single line, then they determine at least n-1 different slopes, where equality is possible only if n is odd and n>3.

Reference: Chapter 9 - The slope problem, from the book - 'Proofs from THE BOOK'.