Question

The equations of two lines are x - 3y = 6 and y = 3x + 2. Determine if the lines are parallel, perpendicular or neither.
i got parallel as an answer?

Answer 1

put equations of two line @ the same form:
y=3x+2
y=1/3 x -2 (you re-wrote first one in this form; see how?)

the slope = coefficient in a front of x
the slope of the first line m1=3
the slope of the second line m2=1/2

parallel lines have the same slope -> your lines are not;
perpendicular lines: m1=-1/m2; NOT perpendicular ;
the answer: neither