Figure 1 - Half planes

Regions I and II in Figure 1 are called open half-planes.
Thus the three regions determined by the line are the open half-planes labeled I and II and the set of points on the line.
The line is called the boundary of each open half-plane.
An open half-plane, along with its boundary, is called a closed half-plane.
Every linear inequality with one or two variables determines an associated linear equation that is the boundary for the solution set of the inequality. For example, 2x+y<=12 has a boundary line 2x+3y=12.