linear algebra

I have questions on subspaces. If someone can be helpful, can you go through one of the questions step by step, so I'll be able to understand how to answer the remainder of the questions. Can you give help in simplistic form, without too much definition, if possible.

is the following a subspace of the real vector R^3?

v = {(x,y,z) : x + 2y = 7z}

Any help will be welcomed.
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