# What is the equation of the line in slope-intercept form that passes through the point (3, –5) and is perpendicular to y = –3x + 4?

Jun 30, 2016

$y = \frac{1}{3} x - 6$

#### Explanation:

$y = - 3 x + 4$ has a slope of $\textcolor{p u r p \le}{- 3}$ (It is in slope-intercept form)
therefore
any line perpendicular to it has a slope of $- \frac{1}{\textcolor{p u r p \le}{- 3}} = \textcolor{g r e e n}{\frac{1}{3}}$

Starting with the slope-point form, with a slope of $\textcolor{g r e e n}{\frac{1}{3}}$ and a point $\left(\textcolor{red}{3} , \textcolor{b l u e}{- 5}\right)$
we have
$\textcolor{w h i t e}{\text{XXX}} y - \left(\textcolor{b l u e}{- 5}\right) = \textcolor{g r e e n}{\frac{1}{3}} \left(x - \textcolor{red}{3}\right)$

$\textcolor{w h i t e}{\text{XXX}} y + 5 = \textcolor{g r e e n}{\frac{1}{3}} \left(x\right) - 1$

$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{g r e e n}{\frac{1}{3}} x \textcolor{b r o w n}{- 6}$

which is the "slope-intercept" form with slope $\textcolor{g r e e n}{\frac{1}{3}}$ and y-intercept color(brown)(""(-6))