Graph the inequality $y\ge x+2.$

The equation of the boundary line is $y=x+2.$ Since the inequality symbol is $\ge ,$ the boundary line is a solid line.

Using $(0,0)$ as the test point, the result is $0\ge 2,$ which is false.

Therefore, the required graph is the region on the side of the boundary line $y=x+2$ that does not include the point $(0,0),$ as shown in the figure below.