# What is the equation of the line that is perpendicular to 2x + 4y = 1 and that passes through the point (6, 8)?

Dec 12, 2016

$y = 2 x - 4$

#### Explanation:

Step 1) Solve for $y$ in order to find the slope of the line in the equation given:

$2 x + 4 y = 1$

$2 x - 2 x + 4 y = 1 - 2 x$

$0 + 4 y = - 2 x + 1$

$4 y = - 2 x + 1$

$\frac{4 y}{4} = \frac{- 2 x}{4} + \frac{1}{4}$

$y = - \frac{1}{2} x + \frac{1}{4}$

Therefore the slope is $- \frac{1}{2}$ and the slope of the perpendicular line is the flipped and negative of this: $- - \frac{2}{1} \to + 2 \to 2$

Step 2) Use the point slope for to obtain the equation for the perpendicular line:

$y - 8 = 2 \left(x - 6\right)$

$y - 8 = 2 x - 12$

$y - 8 + 8 = 2 x - 12 + 8$

$y - 0 = 2 x - 4$

$y = 2 x - 4$