Given a line made by two points (x1, y1) and (x2, y2), its slope (m) is computed as:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]In this case, the points are (-2, -1) and (1, 8). The slope is:
[tex]m_1\text{ = }\frac{8\text{ - (-1)}}{1\text{ - (-2)}}=\frac{9}{3}=3[/tex]Two lines are perpendicular if the multiplication of their slopes is equal to -1. Then:
[tex]\begin{gathered} m_1\cdot m_2=-1 \\ m_2\text{ = }\frac{-1}{m_1} \\ m_2\text{ = }\frac{-1}{3} \end{gathered}[/tex]Isolating y in option D:
2x = -6y +3
2x - 3 = -6y
2/(-6)x - 3/(-6) = y
-1/3x + 1/2 = y
where -1/3 is its slope. Then, this line is perpendicular to line segment AB
