# How do you write an equation of a line going through (3,-1) perpendicular to y=4x+1?

Apr 15, 2018

$x + 4 y + 1 = 0$

#### Explanation:

gradient of the line $y = 4 x + 1$ is $4$

Perpendicular means that the gradient of the line perpendicular to the line $y = 4 x + 1$ is $- \frac{1}{4}$ because the product of the two gradients must equal to $- 1$ ie ${m}_{1} {m}_{2} = - 1$

$\left(y + 1\right) = - \frac{1}{4} \left(x - 3\right)$
$4 y + 4 = - x + 3$
$x + 4 y + 1 = 0$