What is the slope of the line perpendicular and parallel to 7x+2y=-4?

1 Answer
Mar 2, 2018

${m}_{\text{perpendicular")=2/7,m_("parallel}} = - \frac{7}{2}$

Explanation:

• " parallel lines have equal slopes"

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

•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

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

$\text{rearrange "7x+2y=-4" into this form}$

$2 y = - 7 x - 4$

$\Rightarrow y = - \frac{7}{2} x - 2 \text{ with } m = - \frac{7}{2}$

$\Rightarrow {m}_{\textcolor{red}{\text{parallel}}} = - \frac{7}{2}$

$\Rightarrow {m}_{\textcolor{red}{\text{perpendicular}}} = - \frac{1}{- \frac{7}{2}} = \frac{2}{7}$