Linear programming problems involve the use of linear inequalities. In this section, we will see how to draw graphs of linear inequalities in two variable x and y. In section we will use these graphs to solve linear programming problems involving two diction variables.

The graph of a linear inequality in two variables x and y is the set of all points (x, y) for which the inequality holds. The procedure for graphing a linear inequality is as follows:

Step. Graph the corresponding linear equation, a line. This is done by finding nay two points on the line and drawing a straight line through them. For convenience, we choose the two points so that each is on an axis.

Step. Choose a point P not on the line. Normally, this point taken as the origin long at it does not lie on the line. Test P to see whether P satisfies the inequality.

Step. If the coordinates of the chosen point P satisfy the inequality then all points on the same side of the line as the point P satisfy the inequality. If the coordinates of the point P do not satisfy the ine-quality, then all points on the opposite side of the line form P satisfy the inequality.

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