Is -2x+3y=6 parallel, perpendicular, or the same line as 2x-3y=9?

In order to figure this out, you need to get both y's by themselves. Not the most enjoyable thing in the world, but math rarely is. (Make sure to keep them seperate)

3y=2x+6                                                                                          2x-9=3y
y=(2/3)x+2                                                                                       y=(2/3)x-3                                                                                                                
                Do these have the same slope? (number in front of the x)

If the slope is the same, then they are parallel, if one of them flipped and negative, then they would be perpendicular. That is what perpendicular is.-completely opposite.

Hope this helped. Any questions let me know.

The first option would be correct if it were one half and not one