# What is the equation of the line perpendicular to y=-9/16x  that passes through  (-12,5) ?

Apr 9, 2016

$y = \frac{16}{9} x + \frac{79}{3}$

#### Explanation:

The given line is

$y = \frac{- 9}{16} x$

Two Lines are perpendicular if ${m}_{1} \times {m}_{2} = - 1$
Where -

${m}_{1} :$ slope of the given line
${m}_{2} :$ slope of the required line

Then ${m}_{2} = - 1 \times \frac{1}{m} _ 1$

${m}_{2} = - 1 \times \frac{16}{- 9} = \frac{16}{9}$

The equation of the required line is -

$y - {y}_{1} = {m}_{2} \left(x - {x}_{1}\right)$
$y - 5 = \frac{16}{9} \left(x - \left(- 12\right)\right)$
$y = \frac{16}{9} x + 12 \left(\frac{16}{9}\right) + 5$
$y = \frac{16}{9} x + \frac{79}{3}$