Let the slope-intercept form of the line be:

y = mk + b,

where 'm' is the slope and 'b' gives the y-intercept.

If 2 lines are perpendicular, then the product of their slopes is −1.

y + 4x = -12 is equivalent to y = -4x - 12

The slope of y + 4x = -12 is (-4) thus the slope of the perpendicular line will be m = 1/4

Now we can write y = (1/4)x + b. We need to find b.

Since the line y = (1/4)x + b goes trough P(-8,1) we can write

1 = (1/4)*(-8) + b

b = 1 + 2

b = 3

The slope-intercept form of the line that passes through P(-8,1) and is perpendicular to y+4x=-12 is y = (1/4)x + 3.