For each real number $m$, we say that a subset $B$ of $\mathbb{R} \times \mathbb{R}$ is linearly $M$

Question

For each real number $m$, we say that a subset $B$ of $\mathbb{R} \times \mathbb{R}$ is linearly $M$ iff $$\forall (x,y) \in B, y = mx$$

So now the question asked me to give a geometric description of the above set and prove it...

So I am not sure if this is obvious, but isn't $B$ just the set of all lines passing through the origin, with each different $m$, you have a different gradient..

I am not too sure how to "prove it". To me $$B = \{(x,y) \in \mathbf{R} \times \mathbf{R}~|~ y = mx, m \in \mathbf{R}\}$$