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

Mar 17, 2018

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

#### Explanation:

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

•color(white)(x)y=mx+b

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

$y = - 4 x + 3 \text{ is in this form}$

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

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

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

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

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

$\text{to find b substitute "(4,-3)" into the partial equation}$

$- 3 = 1 + b \Rightarrow b = - 3 - 1 = - 4$

$\Rightarrow y = \frac{1}{4} x - 4 \leftarrow \textcolor{red}{\text{perpendicular line}}$