A curve divides a plane into two areas, one satisfying the inequality (shaded) and one that does not (unshaded). So we can pick a point on either side (not on the curve itself) and substitute its x- and y-coordinates into the inequality. If the substituted values make the inequality true, then that point is in the shaded area. Otherwise, that point is in the unshaded area.
We should use a test point to determine the region or regions of the graph of an inequality should be shaded because by plotting an inequality the graph is divided into two regions : one which lie in feasible region and the other does not .
Now in order to check the feasible region we start by taking a test point and see whether it makes the inequality true or not.
If it does not makes the inequality true then that region is not shaded and other is shaded.
If it satisfy the inequality then the region containing that point is shaded.
