# How do you write an equation of a line passing through (0, 4), perpendicular to y=6x-2?

Mar 20, 2018

$y = - \frac{1}{6} x + 4$

#### Explanation:

Perpendicular, in terms of an equation, means that the slope is opposite reciprocal of its original equation

Since the original equation is in terms of $y = m x + b$, where $m = \text{slope}$, the original slope is $m = 6$

Since $6$ can be rewritten as $\frac{6}{1}$, the reciprocal of $6$ is $\frac{1}{6}$, but don't forget the opposite.

Since $\frac{1}{6}$ is positive, the opposite is negative, so the new slope is $m = - \frac{1}{6}$

Since they've given us the point, we can plug that into the original equation to find $b$, the y-intercept:

$\left(4\right) = 6 \left(0\right) + b$
$4 = 0 + b$
$b = 4$

Our y-intercept is $\left(0 , 4\right)$, which you may have noticed is the point they gave us, so that step is technically unneccessary for this particular problem.

Now we can plug in the values we solved for into $y = m x + b$