# What is the equation of the line in slope-intercept form that passes through the point (–2, 4) and is perpendicular to the line y = –2x + 4?

Sep 30, 2017

$y = \frac{1}{2} x + 5$

#### Explanation:

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

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

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

•color(white)(x)y=mx+b

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

$y = - 2 x + 4 \text{ is in this form}$

rArrm=-2" and "m_(color(red)"perpendicular")=-1/(-2)=1/2

$\Rightarrow y = \frac{1}{2} x + b \leftarrow \text{ partial equation}$

$\text{to find b substitute "(-2,4)" into the}$
$\text{partial equation}$

$4 = - 1 + b \Rightarrow b = 4 + 1 = 5$

$\Rightarrow y = \frac{1}{2} x + 5 \leftarrow \textcolor{red}{\text{ in slope-intercept form}}$