Each line plotted on a coordinate graph divides the graph (or plane) into two *half‐planes.* This line is called the *boundary line* (or *bounding line*). The graph of a linear inequality is always a half‐plane. Before graphing a linear inequality, you must first find or use the equation of the line to make a boundary line.

#### Open half-plane

If the inequality is a “>” or “<”, then the graph will be an *open half‐plane.* An open half‐plane does not include the boundary line, so the boundary line is written as a *dashed line* on the graph.

##### Example 1

Graph the inequality *y* < *x* – 3.

First graph the line *y* = *x* – 3 to find the boundary line (use a dashed line, since the inequality is “<”) as shown in Figure 1.