# What is the equation of the line that passes through (-1,3) and is perpendicular to the line that passes through the following points: (6,-4),(5,2)?

Jan 6, 2016

Final answer: $6 y = x + 19$ oe.

#### Explanation:

Defining line that passes through $a : \left(- 1 , 3\right)$ as ${l}_{1}$.
Defining line that passes through $b : \left(6 , - 4\right) , c : \left(5 , 2\right)$ as ${l}_{2}$.

Find the gradient of ${l}_{2}$.
${m}_{2} = \frac{{y}_{b} - {y}_{c}}{{x}_{b} - {x}_{c}} = \frac{- 4 - 2}{6 - 5} = - 6$

${l}_{2} \bot {l}_{1}$

So ${m}_{1} = - \frac{1}{m} _ 2 = - \frac{1}{-} 6 = \frac{1}{6}$

Equation of ${l}_{1}$:
$y - {y}_{a} = {m}_{1} \left(x - {x}_{a}\right)$

$y - 3 = \frac{1}{6} \left(x + 1\right)$

$6 y - 18 = x + 1$

$6 y = x + 19$

Or however you want it arranged.