If the origin lies on the boundary line, which test point is better for deciding shading?

Correct answer: Any point not lying on the line

The direct answer is option A: choose a point that does not lie on the boundary line. To decide shading, substitute the coordinates of a test point into the inequality. A point on the boundary makes the two sides equal, so it only tells us that the point is on the line; it does not tell us which side satisfies the inequality. Therefore choose a convenient point away from the line, such as an intercept-free point that is easy to calculate with, and test it. Option A is correct because such a point lies clearly on one side and identifies the required region. Option B is wrong because the origin is not always suitable; here it lies on the boundary. Option C is wrong because
\((1,1)\) may also lie on the boundary and cannot decide the side. Option D is wrong because a test point is needed when the side is not already obvious. Memory cue: equality means boundary; use a point off the line for shading.