Question

Explain why you can use a test point to determine which region or regions of the graph of an inequality should be shaded.

Answer 1

Answer with explanation:

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.

Answer 2

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.