The set, together with the scalar multiplication and vector addition operations, has to satisfy the axioms of a vector space. Now, in your case, you know already (I assume?) that R^2 is a vector space with "the standard operations". When, therefore, you're trying to determine if a set is a vectorsubspace, your job is a little easier. All you have to do is determine three things:

1. The set is nonempty.

2. The set is closed under scalar multiplication.

3. The set is closed under vector addition.

If those three conditions are satisfied, you've got yourself a subspace. Do those three conditions hold for your set?