Where is the solution region of (y\le -3x+9)?

Correct answer: below the line including it

The direct answer is option D: below the line, including the line itself. The boundary line is \(y=-3x+9\). The inequality says that the chosen point must have a y-value less than or equal to the y-value on the line at the same x. Less than means below; the symbol \(\le\) also includes equality, so the boundary line must be included. Because equality is included, draw the boundary as a solid line, then shade the lower side. Option A is wrong because above the line gives larger y-values, corresponding to \(y>-3x+9\). Option B is wrong because the boundary alone is only the equality \(y=-3x+9\), not all points satisfying the inequality. Option C is wrong because points on both sides do not all satisfy the condition. Option D correctly says below including the boundary. Test point cue: \((0,0)\) gives \(0\le9\), so the side containing the origin is shaded.