Find equation of a line that is perpendicular to another line

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