Solve the given inequality graphically in a two-dimensional plane: $x-y \leq 2$

(N/A) The graphical representation of the line $x-y=2$ is shown in the figure.
This line divides the $xy$-plane into two half-planes.
To determine the solution region,we select a test point not on the line,such as $(0,0)$.
Substituting $(0,0)$ into the inequality $x-y \leq 2$,we get:
$0-0 \leq 2 \implies 0 \leq 2$,which is a true statement.
Since the inequality holds true for the point $(0,0)$,the solution region is the half-plane containing the origin $(0,0)$.
Because the inequality is $\leq$,the line $x-y=2$ is included in the solution region (represented by a solid line).
The solution region is the shaded area shown in the figure.