Answer
Please see the graph, made using graphing software.
Work Step by Step
We treat $x-y>3$ as $x-y=3$ to find where to draw the boundary line.
Let $x=1$
$x-y=3$
$1-y=3$
$1=3+y$
$-2=y$
Let $x=2$
$x-y=3$
$2-y=3$
$-1-y=0$
$-1=y$
Let $x=3$
$x-y=3$
$3-y=3$
$3=3+y$
$0=y$
$(1,-2), (2,-1)$, and $(3,0)$ are on the boundary line.
We try one point not on the line to determine what side of the boundary line to shade.
$(0,0)$
$x-y>3$
$0-0>3$
$0 > 3$ is a false statement, so we shade the side of the line without the point $(0,0)$.