Answer
$y= -2x + \frac13$
Work Step by Step
We are told to find the equation of the line that satisfies the following conditions:
Passes through the point $(\frac12,-\frac23)$, and perpendicular to the line $4x -8y = 1$
To find the equation of the line we must find the slope
then write it in the form:$ y =mx + b$
First solve the given equation for $y$:
$4x - 8y = 1$
$-8y = -4x + 1$
$y = \frac{1}{2}x - \frac{1}{8}$
Since the lines are perpendicular the slope is the negative reciprocal, so the slope of our equation is $m = -2$
$y - (-\frac23) = -2(x-\frac12)$
$y = -2x + 1 - \frac23$
$y= -2x + \frac13$
