# What is the equation of the line perpendicular to y=3x  that passes through  (-1,28) ?

Jan 4, 2016

3y + x - 83 = 0

#### Explanation:

y = 3x has a slope m =3

for perpendicular lines ${m}_{1} \times {m}_{2} = - 1$

$3 \times {m}_{2} = - 1$

 → m_2 = -1/3

equation of perpendicular line : y - b = m(x - a ) , $m = - \frac{1}{3} , \left(a . b\right) = \left(- 1 , 28\right)$

substituting in these values gives
$y - 28 = - \frac{1}{3} \left(x - \left(- 1\right)\right)$

multiply through the equation by 3 will eliminate the fraction

so 3y - 84 = - x - 1

hence 3y + x -83 = 0