## A Line is a Subspace if and only if its $y$-Intercept is Zero

## Problem 663

Let $\R^2$ be the $x$-$y$-plane. Then $\R^2$ is a vector space. A line $\ell \subset \mathbb{R}^2$ with slope $m$ and $y$-intercept $b$ is defined by

\[ \ell = \{ (x, y) \in \mathbb{R}^2 \mid y = mx + b \} .\]

Prove that $\ell$ is a subspace of $\mathbb{R}^2$ if and only if $b = 0$.

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