# How do you write an equation of a line given (12,3) and perpendicular to 3x-y=2?

Dec 15, 2017

$y = \left(- \frac{1}{3}\right) x + 7$

#### Explanation:

take your equation $3 x - y = 2$ and re-write as the standard equation for a line, $y = m x + b$, where m is the slope, and b is the offset. You then have:

$y = 3 x - 2$

...with slope m = 3.

The slope of the line you are trying to find is the negative inverse of this, since we're told that it's perpendicular. This slope is therefore $- \frac{1}{3}$.

You can then solve for the offset in the equation:

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

...you solve for b by plugging in the x value (12) that you are given on the right side, and the y value (3) that you are given on the left:

$3 = \left(- \frac{1}{3}\right) 12 + b$

$3 = - 4 + b$
$7 = b$

so your equation is $y = \left(- \frac{1}{3}\right) x + 7$

GOOD LUCK