Graph the inequality $y\ge 2.$

The equation of the boundary line is $y=2,$ whose graph is a horizontal line that is 2 units above the x-axis. Make this line solid since the inequality symbol is $\ge .$

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

Thus, the graph of $y\ge 2$ is the region on and above the line $y=2,$ as shown in the figure below.