# How do you find a standard form equation for the line with (7,3); perpendicular to the line y = 4x +2?

##### 1 Answer
May 29, 2016

$y = - \frac{1}{4} x + \frac{19}{4}$

#### Explanation:

In general, when two lines $L$ and $L '$ are perpendicular, the slope of the lines are negative inverses of each other.

$m = - \frac{1}{m '}$

The given equation of the line

$y = 4 x + 2$

is in slope-intercept form

$y = m x + b$

where

$m$ is the slope of the line
and $b$ is the $y$-intercept

This means that the slope of the line is

$m = 4$

Hence, the slope of the line perpendicular to the given line is

$m ' = - \frac{1}{4}$

To get the y-intercept, simply substitute the coordinate of the point which we know is on the line

$y ' = m ' x ' + b '$

$y ' = - \frac{1}{4} x ' + b '$

$3 = - \frac{1}{4} \left(7\right) + b '$

$12 = - 7 + 4 b$

$b = \frac{19}{4}$

Hence, the equation of the line is

$y = - \frac{1}{4} x + \frac{19}{4}$