What is the slope of the line perpendicular to  y=-5/3-6 ?

2 Answers
Jan 13, 2018

As asked $y = - \frac{5}{3} - 6 = - \frac{23}{6}$ is a horizontal line; any line perpendicular to it would be vertical and thus have an undefined slope.
If the intended equation was $y = - \frac{5}{3} \textcolor{b l u e}{x} - 6$
see below.

Explanation:

Any equation in the form $y = \textcolor{g r e e n}{m} x + b$ is in slope-intercept form with a slope of $\textcolor{g r e e n}{m}$

If a line has a slope of $\textcolor{g r e e n}{m}$
then all lines perpendicular to it have a slope of $- \left(\frac{1}{\textcolor{g r e e n}{m}}\right)$

If the equation was intended to be
$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{g r e e n}{- \frac{5}{3}} x - 6$
then all lines perpendicular to it will have a slope:
$\textcolor{w h i t e}{\text{XXX}} - \left(\frac{1}{\textcolor{g r e e n}{- \frac{5}{3}}}\right) = \textcolor{m a \ge n t a}{\frac{3}{5}}$

Jan 13, 2018

$\text{slope } = \frac{3}{5}$

Explanation:

$\text{assuming "y=-5/3x-6" is meant}$

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

•color(white)(x)y=mx+b

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

$y = - \frac{5}{3} x - 6 \text{ is in this form with } m = - \frac{5}{3}$

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

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

$\Rightarrow {m}_{\textcolor{red}{\text{perpendicular}}} = - \frac{1}{- \frac{5}{3}} = \frac{3}{5}$