# What is the equation of the line perpendicular to y=-3x  that passes through  (5,8) ?

Feb 20, 2016

Equation of the line perpendicular to $y = - 3 x$ and passing trough $\left(5 , 8\right)$ is $x - 3 y + 19 = 0$.

#### Explanation:

The equation is equivalent to $3 x + y = 0$ and hence equation of a line perpendicular to it will be $x - 3 y = k$.

This is so because for two line to be perpendicular, product of their slopes should be $- 1$.

Using this it is easy to deduce that lines $A x + B y = {C}_{1}$ and $B x - A y = {C}_{2}$ (i.e.just reverse the coefficients of $x$ and $y$ and change sign of one of them) are perpendicular to each other.

Putting the values $\left(5 , 8\right)$ in $x - 3 y = k$, we get $k = 5 - 3 \cdot 8 = 5 - 24 = - 19$

Hence, equation of the line perpendicular to $y = - 3 x$ is $x - 3 y = - 19$ or $x - 3 y + 19 = 0$.