# How do you graph and find the vertex for abs y=x?

In the case of $\left\mid y \right\mid = x$ the vertex is at $\left(0 , 0\right)$
When $y \ge 0$ the equation boils down to $y = x$ - the equation of a ${45}^{o}$ line with slope $1$.
When $y < 0$ the equation boils down to $- y = x$, that is $y = - x$ - the equation of a line with slope $- 1$.