PLEASE HELP ASAP

If a line is perpendicular, then its slope is a negative reciprocal.

First, rearrange the equation so that it's in slope-intercept form.

4x - 12y = 2

4x - 2 = 12y

12y = 4x - 2

y = 1/3x - 1/6

So the negative reciprocal of 1/3x is -3x, so the slope of the new line is -3x.

Tbh at this point it's kind of useless to work out the rest because you can see from the options only one of them has a slope of -3x, and that's the 3rd one.

I'll still work the rest out though:

So you have your half-made equation:

y = -3x + b (the y-intercept)

So you use the given points to substitute in for y and x to find out b.

10 = x; -1 = y

-1 = -3(10) + b

-1 = -30 + b

-1 + 30 = b

29 = b

Therefore, your final equation is y = -3x + 29

Surprise surprise, that's still the 3rd one.