In Step 2 of Example 1, (0, 0) was used as a test point in graphing a linear inequality. Describe those linear inequalities for which (0, 0) is not a valid test point. In that case, how would you choose a test point to make calculation easy?

Data from Example 1

Graph 2x – 3y ≤ 6.

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Step 1 Graph 2x - 3y = 6 as a solid line, since equality is included in the original statement (Fig. 5). -10 -5 10- 5 -10- 2x-3y=6 10 ++++ -10 10 5 in 10 X Figure 5 Figure 6 Step 2 Pick a convenient test point above or below the line. The origin (0, 0) requires the least computation, so substituting (0, 0) into the inequality, we get 2x - 3y = 6 2 (0) 3(0) 0 ≤ 6 This is a true statement; therefore, the point (0, 0) is in the solution set. Step 3 The line 2x - 3y = 6 and the half-plane containing the origin form the graph of 2x - 3y = 6, as shown in Figure 6.