For the inequality y > 2x + 2, how should you shade on the graph?

For the inequality y > 2x + 2, how should you shade on the graph?

• A. Dotted boundary, shading above
• B. Solid boundary, shading above
• C. Solid boundary, shading below
• D. Dotted boundary, shading below

Answer: (A)

When graphing a linear inequality in two variables, the boundary line is drawn as a dashed (dotted) line if the inequality is strict (no equal sign). Here the boundary is y = 2x + 2, and since the inequality is y > 2x + 2, the line is not included. The region that satisfies the inequality is where y is greater than 2x + 2, which is the area above that line. You can confirm this by testing a point known to be above, say (0,3): 3 > 2(0) + 2, which is true, so that region is shaded. So the correct description is a dotted boundary with shading above.

When graphing a linear inequality in two variables, the boundary line is drawn as a dashed (dotted) line if the inequality is strict (no equal sign). Here the boundary is y = 2x + 2, and since the inequality is y > 2x + 2, the line is not included.

The region that satisfies the inequality is where y is greater than 2x + 2, which is the area above that line. You can confirm this by testing a point known to be above, say (0,3): 3 > 2(0) + 2, which is true, so that region is shaded.

So the correct description is a dotted boundary with shading above.