Which statement about the boundary line and shading is correct for x+4y>8?

Correct answer: dashed line and opposite to origin

Two graphical conventions govern this question. First, a strict inequality such as > does not include its boundary, so the equation x+4y=8 must be drawn as a dashed line rather than a solid line. Second, use a test point to choose the half-plane. The origin gives 0+4(0)=0, and 0>8 is false. Thus the origin side is not the solution side; the region opposite the origin must be shaded. Equivalently, points with x+4y greater than 8 are selected. Therefore option C is correct. Options A and B incorrectly use a solid boundary, which would represent ≥ or ≤. Option D uses the dashed line correctly but shades the wrong side because the origin fails the inequality.