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.
