These lines would be perpendicular.
If we divide 3y+7 by 12, we would get 1/4y+7/12
Now, if we re arange for y, we get: y=-1/4x+7/3
In this case, the y intercept (7/3) does not matter, only the slope does. The slope must be the opposite reciprical of the other slope. For instace if the slope was 4, the perpendicular lines slope must be -1/4. That is the exact case we have above.
Really hope that I helped :)
Let me know if you have any furthere questions!
-CSX
