How to graph an absolute value equation?

Question

How would you graph:

$|x+y|=1$ ? I can do the normal $y=|x+1|$ and all that. But how would you do a question with two of these unknowns in the absolute value?

Any help would be greatly appreciated, thanks.

Answer 1

It doesn't seem as though $|x+y|=1$ is a function, since for $x=2$, the values $y=-1$ and $y=-3$ both satisfy the equation.

The way to graph this would be to graph two individual equations: $x+y=1$ and $x+y=-1$ (these two equations result when we lift the absolute value). So we graph separately: $$y=-x+1$$$$y=-x-1$$