Let \(\mathbb R\) be the set of real numbers. We denote by \(\mathcal F\) the set of all functions \(f\colon\mathbb R\to\mathbb R\) such that

\[f(x + f(y)) = f(x) + f(y)\]

for every \(x,y\in\mathbb R\) Find all rational numbers \(q\) such that for every function \(f\in\mathcal F\), there exists some \(z\in\mathbb R\) satisfying \(f(z)=qz\).