4. (5 points) Consider the subset S=\left\{(x, y) \in \mathbb{R}^{2}: \exists m, n \in \mathbb{Z}, \text { not both zero, s.t. } m x+n y=0\right\} \subset \mathbb{R}^{2} That is, S

is the set of points in R? that lie on a line through the origin with rational slope. Is S a subspace of R?? Prove your assertion.