Determining Correct Shading of Half Planes on a Graph

The video tutorial explains how to determine if a half plane on a graph is correctly shaded by checking if a solution in the half plane makes the inequality true. It covers graphing inequalities, using points on the line, verifying shaded regions, and using the coordinate (0,0) for verification. The tutorial emphasizes that choosing a solution from the shaded region or using (0,0) can confirm correct shading.

Why is it important to choose a point from the shaded region when verifying the inequality?

What does it indicate if the point (0,0) is not in the shaded region of the graph?

Summarize the methods to ensure that the correct half plane is shaded in a graph of an inequality.