The given inequality is $x-y \leq 2$
Consider the equation $x-y =2$
we see that $(2,0) $ and $( 0,-2)$ satisfy the equation .
The graphically representation of the line $x-y =2$ is given below.
The line $x-y =2$ divides the xy plane into two half plane I and II
We select a point (0,0) in half plane I
We see that $ 0-0 \leq 2$
$ 0 \leq 2$ is true.
Therefore the half plane II is not a solution region.
The half plane I containing the point (0,0) is the solution region represented by the shaded region including the points on the line .