The problem statement as given is y - 3x = 1y. That's a little strange because we could subtract y from both sides of the equation and y would disappear completely, leaving us with -3x = 0.
Perhaps the correct problem statement is y - 3x = 1. This is just a guess and so could be wrong. But it allows us to look at how to solve similar problems.
I suggest putting the problem into standard slope-intercept form. That's a good idea when answering questions involving slopes. Slope-intercept form means working on the equation to get it into a form that shows y = mx + b, where m is the slope and b is the intercept.
To do this for our equation, we can add 3x to both sides of the equation to get y = 3x + 1. We note that our slope is 3 since 3 is the coefficient on the x term when the equation is put into standard slope-intercept form.
All lines parallel to this line must have the same slope. So, all parallel lines will have a 3x term when put in standard slope-intercept form. The only answer that meets that requirement is D. y = 3x + 2.
