Answer
$y=\frac{1}{4}\times x - \frac{7}{2}$
Work Step by Step
Find out the equation in Slope-intercept form of
$4x + y = \frac{2}{3}
$
Subtract y from both sides and you get
$4x = \frac{2}{3} - y$
Now subtract $\frac{2}{3}$ from both sides
$4x - \frac{2}{3} = -y$
Divide $-1$ from each side
$-4x + \frac{2}{3} = y$
Now you need to find out the slope of the perpendicular line.
If you multiply the slopes of two perpendicular lines, you should get $-1$
$-1 \div -4 = \frac{1}{4}$. $\frac{1}{4}$ is the slope of the perpendicular line. So far the equation looks like this:
$ y = \frac{1}{4} \times x + b$
If you substitute the coordinates given in the problem, then we get
$ -3 = \frac{1}{2} + b$
Therefore $ b = -\frac{7}{2}$
So now we got
$y = \frac{1}{4} \times x - \frac{7}{2} $
