# What is the equation of the line perpendicular to y=-2/15x  that passes through  (-4,24) ?

Apr 13, 2016

$y = \frac{15}{2} x + 54$ or $y = 7.5 x + 54$

#### Explanation:

The line $y = - \frac{2}{15} x$ has a slope of $m = - \frac{2}{15}$

The perpendicular slope of $m = - \frac{1}{m}$

Therefore the perpendicular line would have a slope of $m = \frac{15}{2}$

The point-slope equation of a line is

$\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$

The perpendicular line passes through $\left(- 4 , 24\right)$

$y - 24 = \frac{15}{2} \left(x - \left(- 4\right)\right)$

$y - 24 = \frac{15}{2} x + 30$

$y = \cancel{- 24} \cancel{+ 24} = \frac{15}{2} x + 30 + 24$

$y = \frac{15}{2} x + 54$ or $y = 7.5 x + 54$