The slope of the perpendicular line is the negative reciprocal of the slope of the original line. The perpendicular line with the opposite y-intercept has equation
... y = (-1/m)x - b
The point of intersection is where the x- and y-values are equal, so ...
... mx + b = (-1/m)x - b
... (m +1/m)x = -2b . . . . . . . add 1/m - b to both sides
... (m²+1)x = -2bm . . . . . . . multiply by m
... x = -2bm/(m²+1) . . . . . . divide by the coefficient of x
