Answer
Please see the graph, made using graphing software.
Work Step by Step
$-x \leq y$
To find the boundary line, replace the $\leq$ sign with the $=$ sign.
$-x=y$
Let $x=2$
$-x=y$
$-2=y$
Let $x=-4$
$-x=y$
$-(-4)=y$
$4=y$
Let $x=5$
$-x=y$
$-5=y$
$(2,-2), (-4,4)$, and $(5,-5)$ are on the line.
Use $(1,1)$ to determine what side of the line to shade.
$-x\leq y$
$-(1) \leq 1$
$-1 \leq 1$ is true, so we shade the side of the line with $(1,1)$.