Graph each inequality.

$y<2$

The graph of a linear inequality in two variable (say, $x$ and $y$), first get $y$alone on one side. Then consider the rotated equation obtained by changing the inequality sign to an equality sign. The graph of this equation is a Line. If the inequality is strict $<or>$,graph dashed line. If the inequality is not strict $\le or\ge$,graph a solid line.

Finally, pick one point that is not a either line $(0,0)$ is usually the easiest and decide whether these co-ordinate satisfy the inequality or not. If they do, shade the half-plane containing that point. If they don’t shade the other half plane.

Let a inequality $y\le x-2$. Now put $(0,0)$in $y\le x-2$which implies $0\le -2$, hence the inequality is not satisfied for the graph of $y\le x-2$

Hence the graph of $y<2$