# How do you write an equation of a line passing through (2, 4), perpendicular to y + 4x= 5?

Jul 14, 2016

$x - 4 y + 14 = 0$

#### Explanation:

Let us write the equation $y + 4 x = 5$ in slope intercept form as $y = - 4 x + 5$. Hence it's slope is $- 4$.

Now, the product of slopes of two lines perpendicular to each other is $- 1$, hence as one line has slope $- 4$, line perpendicular to it will have a slope of $\frac{- 1}{- 4} = \frac{1}{4}$.

As equation of a line passing through $\left({x}_{1} , {y}_{1}\right)$ and slope of $m$ is

$\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$,

Equation of a line passing through $\left(2 , 4\right)$ and having a slope of $\frac{1}{4}$ is

$\left(y - 4\right) = \frac{1}{4} \left(x - 2\right)$ or

$4 y - 16 = x - 2$ or

$x - 4 y + 16 - 2 = 0$ or

$x - 4 y + 14 = 0$