# How do you write the equation of a line in slope intercept form that is perpendicular to the line y = –4x and passes through the point (2, 6)?

Mar 7, 2018

$y = \frac{1}{4} x + \frac{11}{2}$

#### 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

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

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

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

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

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

$\text{to find b substitute "(2,6)" into the partial equation}$

$6 = \frac{1}{2} + b \Rightarrow b = \frac{12}{2} - \frac{1}{2} = \frac{11}{2}$

$\Rightarrow y = \frac{1}{4} x + \frac{11}{2} \leftarrow \textcolor{red}{\text{in slope-intercept form}}$