Select the equations of the lines that are parallel to the line whose equation is y = 3x + 5

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.