Solve the given inequality $x \geq y-2$ graphically in two - dimensional plane.
The graphical representation of $x \geq y-2$ is given by blue dotted line in the figure below.
This lines divides $x-y$ plane into two parts.
Select a point (not on the line), which lies on one of the two parts, to determine whether the point satisfies the given inequality or not.
We select the point as $(0,0)$
It is observed that $0>0-2$ or $0>-2$ which is false.
Therefore, the solution for the given inequality excluding the points on the line.
This can be represented as follows,