SMO 1998 Problem 2

Let $N$ be the set of natural numbers, and let $f: N \to N$ be a function satisfying $f(x) + f(x + 2) < 2 f(x + 1)$ for any $x \in N$ . Prove that there exists a straight line in the $xy$ -plane which contains infinitely many points with coordinates $(n,f(n))$ .