Algebra I

Each line drawn on the coordinate graph divides the graph (or plane) into two half-planes. This line is called the boundary line (or limit line). The graph of a linear inequality is always a half plane. Before plotting a linear inequality, you must first find or use the equation of the line to create the boundary. Open half-plane If the inequality is “>” or “<”, then the graph will be an open half-plane. An open half plane does not include a boundary, so the boundary is written as a dashed line on the graph Read: what is a half plane Example 1 Graph the y inequalityNow shade the lower half of the plane as shown in Figure 2, since yTo check if you’ve shaded the half-plane correctly, plug in a coordinate pair — the (0, 0) pair is usually a good choice. If the coordinates you have chosen make the inequality a true statement when plugged in, you should shade the half-plane containing those coordinates. If the coordinates you have chosen do not make the inequality a true statement, then shade the half-plane that does not contain those coordinates.Since y ≥ 2 x, you should paint the upper half plane. If in doubt or to check, plug in a pair of coordinates. Try pairs (1, 1).So you should fill in the half-plane that does not contain (1, 1) as shown in Figure 4. Figure 4. Graph of the y ≥ 2 x inequality.Read more: what are the most common multiples of 3 and 6

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