The slope of line Line B D is StartFraction 2 b Over 2 a minus c EndFraction. Triangle A B C with centroid G is shown on an x and y-axis. Lines are drawn from each point through the centroid to the midpoint of the opposite side to form line segments A F, B D, and C E. Point A is at (0, 0), point D is at (c, 0), point C is at (2 c, 0), point B is at (2 a, 2 b), and point E is at (a, b).

What is the equation of Line B D, simplified?