So if the new line is perpendicular, then you will use the inverse. If our original equation is 4x-12y=2, then we need to simplify that first. I prefer to keep x on the left, so our new equation would be 4x=12y+2, which simplifies down to x=3y+0.5 so now we take the inverse of that. Keep in mind, all numbers are truly just fractions with a denominator of 1. Now we can use that to find our new equation. Our original slope is 3 so the inverse of said intercept would be 1/3. Our new slope is -2 because that is the inverse of 1/2, however we make it opposite because we do the opposite of our original equation. Our new equation would be x=1/3y-2 I believe. I might be wrong though. I could be totally off too