# How do you write an equation of a line passing through (1, 5), perpendicular to y + 4x = 7?

Mar 13, 2018

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

#### Explanation:

$\text{The equation of a line in "color(blue)"slope-intercept form}$ is.

•color(white)(x)y=mx+b

$\text{where m is the slope and b the y-intercept}$

$\text{Rearrange "y+4x=7" into this form}$

$\text{subtract 4x from both sides}$

$y \cancel{+ 4 x} \cancel{- 4 x} = - 4 x + 7$

$\Rightarrow y = - 4 x + 7 \leftarrow \textcolor{b l u e}{\text{in slope-intercept form}}$

$\text{with slope m } = - 4$

$\text{Given a line with slope m then the slope of a line}$
$\text{perpendicular to it is}$

•color(white)(x)m_(color(red)"perpendicular")=-1/m

$\Rightarrow {m}_{\text{perpendicular}} = - \frac{1}{- 4} = \frac{1}{4}$

$\Rightarrow y = \frac{1}{4} x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

$\text{To find b substitute "(1,5)" into the partial equation}$

$5 = \frac{1}{4} + b \Rightarrow b = \frac{20}{4} - \frac{1}{4} = \frac{19}{4}$

$\Rightarrow y = \frac{1}{4} x + \frac{19}{4} \leftarrow \textcolor{red}{\text{equation of perpendicular}}$