Section 15.2: Graphing Half-Planes

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15.2 Outline

    1. half-plane
    2. boundary
    3. open/closed
  2. Procedure for graphing a linear inequality

 

15.2 Essential Idea

Procedure for graphing a linear inequality

Step 1
Graph the boundary. Replace the inequality symbol with an equality symbol and draw the resulting line. This is the boundary line. The boundary line is solid when the boundary is included (less than or equal to; greater than or equal to). The boundary line is dashed when the bound is not included (less than; greater than).

Step 2
Test a point. Choose any point in the plane that is not on the boundary line; the point (0, 0) is usually the simplest choice. If this test point makes the inequality true, shade the half-plane which contains the test point. That is, the shaded (highlighted) plane is the solution set. If the test point makes the inequality false, shade the other half- plane for the solution.