you find a perpendicular line by getting the "opposite reciprocal" of the given slope. in this case, the given slope is 2 (which you get from the given equation).
the "opposite reciprocal" means the opposite sign, and the reciprocal of the number. in the case of 2, the opposite reciprocal is (-1/2). this is your new slope.
m = (-1/2) and P(-9, 6)
from here, all you have to do is plug it into point-slope form: (y - y1) = m(x - x1)
y - 6 = (-1/2)(x + 9) --- distribute (-1/2)
y - 6 = (-1/2x) - (9/2) --- add 6 to both sides
y = (-1/2x) + (3/2) --- this is your slope-intercept form equation
