A. Graphing Linear Inequalities in Two Variables
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A. Graphing Linear Inequalities in Two Variables
In the previous Investigation, you explored inequalities in two variables and their corresponding graphs. You may have found that graphing the corresponding equation produced a line that separated the region of points that made the inequality true from the region of points that made the inequality false. The solution region is the section of points that make the inequality true, and the dividing line is called the boundary. A graph of the inequality \(x - 3y \ge 1\) is shown.
A dashed boundary is used to represent a strict inequality, where values on the line are not included in the solution region.
A solid boundary is used to represent an inequality that is not strict, where the values on the line are included in the solution region.
Knowing that a solution region has the corresponding equation as a boundary allows you to sketch the graph of an inequality in two variables fairly quickly.
A dashed boundary is used to represent a strict inequality, where values on the line are not included in the solution region.
A solid boundary is used to represent an inequality that is not strict, where the values on the line are included in the solution region.
Knowing that a solution region has the corresponding equation as a boundary allows you to sketch the graph of an inequality in two variables fairly quickly.