# What is the equation of a line that is perpendicular to y=2x+4 and passes through the point (4,6)?

Dec 14, 2016

$y = - \frac{1}{2} x + 8$

#### Explanation:

To start, any question that asks you for a line perpendicular to another, you should know that the slope of the new line will be the negative reciprocal of the slope given

In your case the opposite of 2x is $\frac{1}{2} x$ and then we make it negative to get $- \frac{1}{2} x$

from here, you have enough information to solve the problem using point slope form. which is $y - y 1 = m \left(x - x 1\right)$

now we plug in what we are given: $y 1$ is 6, the slope (m) is $- \frac{1}{2} x$ and $x 1$ is 4.

Now, we should have $y - 6 = - \frac{1}{2} \left(x - 4\right)$

Next, we distribute the $- \frac{1}{2} \left(x - 4\right)$ and get $- \frac{1}{2} x + 2$

our equation at this point is now $y - 6 = - \frac{1}{2} x + 2$

Finally we just have to add the -6 from both sides to get $y$ alone.

Our FINAL equation is $y = - \frac{1}{2} x + 8$

Hope this helps!!