Step 1:

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.

Step 2:

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.

Step 3:

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 .