# What is the slope of a line perpendicular to Ax+By+C=0?

Jul 31, 2016

$B x - A y + C = 0$

#### Explanation:

Given -

$A x + B y + C = 0$

In such case you have to interchange the co-efficients of $x$ and $y$ and then change the sign of the coefficient of $y$

The equation of the perpendicular line is

$B x - A y + C = 0$

You can check it by using the formula

${m}_{1} \times {m}_{2} = - 1$

Slope of the first line -

${m}_{1} = - \frac{a}{b} = - \frac{A}{B}$

Slope of the second line -

${m}_{2} = - \frac{a}{b} = - \frac{B}{- A} = \frac{B}{A}$

Substituting these values in the formula ${m}_{1} \times {m}_{2} = - 1$

We get -

$- \frac{\cancel{A}}{\cancel{B}} \times \frac{\cancel{B}}{\cancel{A}} = - 1$