For two lines to be parallel to each other they must have the same slope. Our reference line is of the form y=mx+b where m is the slope.
y=3x+5
So any line that has a slope of 3 will be parallel...
6x-2y=12
-2y=-6x+12
y=3x-6, so this line is parallel..
...
-3x-y=8
-y=3x+8
y=-3x+8, so this line is not parallel
...
3y=9x
y=3x, so this line is parallel
...
y=-x/3, so this line is not parallel.
Thus the first and third lines are parallel to our reference line because they all have a slope of 3.
