#### Answer

The equation is symmetric about the $x$-axis, the $y$-axis and the origin.

#### Work Step by Step

$|x|+|y|=1$
Check for symmetry about the $y$-axis by substituting $x$ by $-x$ in the given function and simplifying:
$|-x|+|y|=1$
$|x|+|y|=1$
Since substituting $x$ by $-x$ yielded an equivalent expression, the equation is symmetric about the $y$-axis.
Check for symmetry about the $x$-axis by substituting $y$ by $-y$ in the given function and simplifying:
$|x|+|-y|=1$
$|x|+|y|=1$
Since substituting $y$ by $-y$ yielded an equivalent expression, the equation is symmetric about the $x$-axis.
Since the equation is symmetric about both the $x$ and $y$-axis, it is also symmetric about the origin.
The graph is shown in the answer section.