Linear Inequalities in two Variables

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In this section, we review how to graph a linear inequality in two variables. A linear inequality in two variables is of the form: ax + by < c, where a, b, and c are real numbers, a and b are not both zero, and < could be: >, ≥, or ≤. To graph a linear inequality in two variables, we solve the inequality for y. We then replace the inequality symbol with an equality symbol and graph the resulting equation. This gives us our boundary line. The boundary line separates the solution region from the non-solution region. The boundary line is dashed for a strict inequality and solid for a non-strict inequality. If our inequality is strict, the boundary line is not part of the solution. Therefore a dashed line shows this line is excluded from the solution region. If the inequality is non-strict, we draw a solid line to show the line is included. Once the boundary line is drawn, we shade below the line for a less than and above the line for a greater than. Note this only works when we have solved the inequality for y. If we don’t solve the inequality for y, we use a test point. The test point method tells us to choose a point on either side of the line. If that point works as a solution to the inequality, the test point lies in the solution region and that region should be shaded. If the point does not work, the test point lies in the non-solution region and we must shade the other region.
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