Test Point
Completion requirements
Test Point
Using a test point is one way to decide which region of an inequality’s graph to shade. Another method is to isolate one variable of the inequality, and then interpret the resulting inequality. For example, in the inequality \(y \ge -\frac{3}{2}x - 5\), the line \(y = -\frac{3}{2}x - 5\) represents the boundary, and the solution region includes \(y\)-values that are greater than or equal to those represented on the line. Larger \(y\)-values are further up on the graph, so shade the region above the line. Similar logic can be used for other isolated variables.
If you decide to use this method to determine the solution region, make sure to interpret the inequality correctly. The inequality symbol cannot be used by itself to determine the solution region.
Do you expect to shade above or below the line for an inequality of the form ______\(\gt y\)?
If you are unsure, check with a test point.