You can put this solution on YOUR website! The slope of
-x + 6y = 30
is found by either solving for y or by reading -A/B...
6y = x + 30
y = (1/6)x + 5
Our slope is 1/6.
Then plug our new point and wanted slope into
y = mx + b and get
-6 = (1/6)(-6) + b
b = -5
so our equation is
y = (1/6)x - 5