# How do you find the slope perpendicular to x + 2y = 7?

May 27, 2018

$\text{perpendicular slope } = 2$

#### Explanation:

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

•color(white)(x)y=mx+b

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

$\text{rearrange "x+2y=7" into this form}$

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

$2 y = - x + 7$

$\text{divide all terms by 2}$

$y = - \frac{1}{2} x + \frac{7}{2} \leftarrow \textcolor{b l u e}{\text{in slope-intercept form}}$

$\text{with slope m "=-1/2} \mathmr{and} b = \frac{7}{2}$

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

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

m_("perpendicular")=-1/(-1/2)=2larrcolor(red)"perpendicular slope"