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

Toolbox:
• To represent the solution of linear inequality of one or two variable in a plane if the inequality involves $'\geq'$ or $' \leq$ we draw the graph of the line as a thick line to indicate the line is included in the solution set.
• If the inequality involves $'>'$ as $'<'$ we draw the graph of the line using is not included in the solution set.
• To solve an inequality $ax+by > c \qquad a \neq 0, b \neq 0 ( or \;> )$
• We consider the corresponding equation $ax+by =c$ which represents a straight line This line divides the plane into two half planes I and II
• We take any point in I half plane and check if it satisfies the given inequality will be one half plane (called solution region ) Containing the point satisfying the inequality
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 .