The equations of two lines are x - 3y = 6 and y = 3x + 2. determine if the lines are parallel, perpendicular or neither.

Start by converting x - 3y = 6 into slope-intercept form:
x - 3y = 6
Subtract x from both sides:
-3y = -x + 6
Divide both sides by -3:
y = (1/3)x - 2
Now compare both equations:
y = (1/3)x - 2
y = 3x + 2
They don't share anything perpendicular or parallel equations would share, so therefore they are neither.

Hope this helps! :)