Verified answer

ax + by = c => slope = -a/b

Line 1: x + 3y = 6 => slope = -1/3

If the second line is parallel to this first one, than their slopes are equal, so L2's slope is -1/3 ( L2 = Line 2).

L2 passes through (6, -2):

y - (-2) = slope*(x - 6)

But slope = -1/3, so:

y + 2 = -1/3 (x-6)

3y + 6 = 6 - x

x + 3y = 0.

Parallel lines have the same slope as the original line, so with all this information, you can create an equation in point-slope form.

y - y1 = m(x - x1)

y - (-2) = 3(x - 6)

y +2 = 3x - 18

y = 3x -20