Let ax+by=c be the given(known) line
slope of this line (m₁) = -a/b
Let m₂ be the slope of required line
Since given line and required line are perpendicular to each other, the product of their slopes must be equal to -1
Therefore, m₁.m₂ = -1
(-a/b)m₂ = -1
m₂ = b/a
Therefore, by slope-intercept form, line perpendicular to given line can be given by,
y=m₂x+c
y=(b/a)x+c
Therefore, ay-bx=c
or bx-ay+c = 0
Where c is constant and it can be determined according to the conditions given in questions.
Therefore the required line is,
bx-ay+c=0
