Determine if the lines 2y-6x -2= 0 and the line -3y+9x +3 =0 are parallel ?

To determine if two lines are parallel or not, we need to find
the slope for each line.

If the slopes are equal, then the lines are
parallel.

First we will need to rewrite the equations of the lines
into the slope form y= mx + b such that m is the slope.

For equation
(1):

2y - 6x -2 = 0

==> 2y= 6x
+2

==> y= 3x +1

==> Then
the slope is m1= 3...........(1)

For equation
(2):

-3y + 9x +3 = 0

==> -3y =
-9x -3

==> y= 3x + 1

==>
m2= 3 ............(2)

Then we notice that the
equations of the lines are the same. Then the lines are
parallel.