This is only a subspace if $b=0$ - Axler - LADR p13

Question

I have written here in Axler - Linear Algebra Done Right, page $13$.

If $b\in \mathbb{F}$, then $\{(x_1,x_2,x_3,x_4)\in \mathbb{F}^4: x_3 = 5x_4 + b\}$ is a subspace of $\mathbb{F}^4$ if and only if $b=0$

I am not sure what this is getting at. Why is this the case?

Answer 1

A subspace must contain the zero vector.