Final answer:
To find a test point for the inequality 2/3x - 2y ≥ 1, any point not on the boundary can be used, and the shaded area will be on the side of the boundary line where the inequality holds true.
Step-by-step explanation:
To find a test point that holds true for the inequality 2/3x - 2y ≥ 1, you can pick any point that is not on the boundary line 2/3x - 2y = 1. Substitute the x and y values of the point into the inequality to see if the inequality holds. As for the shaded area, it represents all the points that satisfy the inequality. To find where this area lies, we first graph the boundary line, making it solid because the inequality includes the equal case (i.e., ≥). Then we choose a test point, like (0,0), and substitute it into the inequality. If the inequality is true, then the area containing the origin will be shaded; if false, the opposite side of the line will be shaded.