let the first line equation be

y = k1*x + b1

then the perpendicular line will be

y = k2*x + b2

we use the facts that 2 lines are perpendicular if the product of their slopes is -1

k1*k2 = - 1

if k1 = m then k2 = -1/m, for some m = constant. and m <> 0

b1 <> 0, b2<>0 otherwise the lines will pass through the origin (0, 0)

for x = 0 the lines have the same y-intercept that is

b1 = b2 = b

Thus the equations of the lines are

first line

y = m*x + b

second line

y = - x/m + b

where b <> 0, m <> 0.