# How do you determine the equation of the line passing through (2,6) That is perpendicular to y=-3x+1?

Apr 8, 2018

color(violet)("Equation of the perpendicular line is " 3y = x + 16

#### Explanation:

Given $y = - 3 x + 1$

It is in the form, $y = m x + c$ where m is the slope & c the y-intercept.

$\therefore m = - 3$

Slope of perpendicular line ${m}_{1} = - \frac{1}{m} = \frac{1}{3}$

Equation of perpendicular line passing thru (2,6) is

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

$y - 6 = \left(\frac{1}{3}\right) \cdot \left(x - 2\right)$

$3 y - 18 = x - 2$

$3 y = x + 16$