How is the boundary line drawn for the inequality (x+y\leq 6)?

Correct answer: Solid line

The direct answer is option A, a solid line. The inequality is \(x+y\le6\). Its boundary is \(x+y=6\). Because the sign is \(\le\), points on the boundary satisfy the inequality exactly and must be included in the solution. An included boundary is drawn with a solid line. Option A is therefore correct. Option B, a dashed line, is used for strict inequalities such as \(<\) or \(>\), where boundary points are excluded. Option C, points only, does not show the complete boundary line. Option D, no line, is wrong because the boundary is needed to separate the solution region. The region would be selected using a test point, but the line itself remains solid. Memory cue: less-than-or-equal or greater-than-or-equal means solid; strict signs mean dashed.