Answer
$W$ is a subspace of $R^2$.
Work Step by Step
Let $W$ be a subset of $V$ such that
$$W=\{(x, y) : x=2 y\}, \quad V=R^{2}.$$
Assume that $u=(2a,a), v=(2b,b)\in W$ and $c\in R$. Now, we have
(a) $W$ contains the zero vector $(0,0)$.
(b)\begin{align*}
u+v&=(2a,a)+(2b,b)\\
&=(2a+2b,a+b)\\
&=(2(a+b),a+b)\in W.
\end{align*}
(c) $cu=c(2a,a)=(2ca,ca)\in W$.
Hence, $W$ is a subspace of $R^2$.
