Let $f:\mathbb R \rightarrow \mathbb R$ continuous function such that $f(x+y)=f(x)+f(y)$. Then there exist a real $r$ such that $f(x) = r x$.
I need to find all functions $f:\mathbb R \rightarrow \mathbb R$ which are continuous and satisfy $f(x+y)=f(x)+f(y)$