What is the boundary line of the inequality (x+y\leq 6)?

Correct answer: (x+y=6)

The direct answer is option A, \(x+y=6\). A boundary line separates the shaded solution region from the non-solution region. To obtain it, replace the inequality sign by equality: \(x+y\le 6\) becomes \(x+y=6\). The line passes through \((6,0)\) and \((0,6)\). Option A is exactly this line. Option B, \(x-y=6\), has a different slope and represents another line. Option C, \(x+y<6\), is still an inequality and describes a region rather than the boundary equation itself. Option D, \(x=6\), is a vertical line and ignores y. The symbol \(\le\) later tells us to include the boundary and shade the side containing a test point such as \((0,0)\). Memory cue: boundary means change < or \(\le\) into = first.