Table of Contents Graphing Linear Inequalities in Two Variables A linear inequality in two variables takes one of the following forms: The solution of a linear inequality is all ordered pairs (x, y) that satisfy the inequality.

Table of Contents Example 1 Consider the linear inequality … The ordered pair (8, - 4) is not a solution: False

Table of Contents The ordered pair (8, 6) is a solution: True

Table of Contents To graph a linear inequality in two variables: 1)Put an equals sign in place of the inequality sign and graph the line. If the inequality symbol is, graph a dashed line. If the symbol is ≤ or ≥, graph a solid line. The line divides the plane into two half-planes.

Table of Contents 2)Try a test point that is not on the line in the original inequality. If the point satisfies the inequality, then shade in the half-plane that contains the point. If the point does not satisfy the inequality, then shade in the half-plane that does not contain the point.

Table of Contents Example 2 Graph: Create the equation. Graph the line by the method of your choice: 1.Solve for y and use the slope-intercept method to graph. 2.Find the points (0, y) and (x, 0) and graph the line through them. Since the < symbol is used, draw a dashed line.

Table of Contents Select a point not on the line.

Table of Contents Check the point in the original inequality. True

Table of Contents Since the point satisfied the inequality, shade in the same side that the point is on.

Table of Contents Example 3 Graph: Create the equation. Since the ≤ symbol is used, draw a solid line. Graph the line. Recall that the graph of x = c is a vertical line.

Table of Contents Select a point not on the line.

Table of Contents Note that once again we have selected the origin, because it is the easiest to evaluate in the inequality. The only time we won’t choose the origin is when the line itself (dashed or solid) passes through the origin. Any point not on the line can be used, but the origin is very convenient.

Table of Contents Check the point in the original inequality. False

Table of Contents Since the point did not satisfy the inequality, shade in the opposite side that the point is on.

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