Write a system of inequalities for the graph
Checking points M and N yield true statements. Determine if the boundary line should be dotted or solid that is, check whether the inequality is strict or inclusive, respectively.
How to write an inequality from a graph
In order to graph a linear inequality, we can follow the following steps: Graph the boundary line. If the inequality is of the form then the region above the line is shaded and the boundary line is solid. Graphically, we can represent a linear inequality by a half-plane, which involves a boundary line. The purple area shows where the solutions of the two inequalities overlap. A strict inequality, such as would be represented graphically with a dashed or dotted boundary line. On one side lie all the solutions to the inequality. We can use the method described above to find each linear inequality associated with the boundary lines for this region. Checking points M and N yield true statements. The boundary line is precisely the linear equation associated with the inequality, drawn as either a dotted or a solid line. This is an inclusive inequality since it can be interpreted as or meaning we wish to include the equality. Choose a test point not on the boundary line. For example, in Figure 1, the linear inequality is represented on the coordinate plane.
On the other side, there are no solutions. Use the test point to determine which half-plane should be shaded. You can check a couple of points to determine which side of the boundary line to shade. If the inequality is of the form then the region above the line is shaded and the boundary line is solid.
Notice that it is not true that and so we shade the half-plane that does not include the origin. We can use the method described above to find each linear inequality associated with the boundary lines for this region.
Graphing a System of Two Inequalities The graph of a single linear inequality splits the coordinate plane into two regions.
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