#### Answer

$\frac{1}{2}x+y=\frac{-1}{3}$

#### Work Step by Step

Perpendicular lines have slopes that are negative reciprocals of each other.
Write the equation in slope-intercept form
$y=2x-4$
The given line has a slope of $2$
This means that the slope of the line perpendicular to it is $\frac{-1}{2}$
Thus, the tentative equation of the line is
$y=\frac{-1}{2}x+b$
The line is said to have a x-intercept of $\frac{-2}{3}$ so $b=\frac{-2}{3}$
Therefore the equation of the line perpendicular to the given line is $y=\frac{-1}{2}(x-\frac{-2}{3})$
Convert this to $ax+by=c$ form to have:
$y=\frac{-1}{2}x-\frac{2}{6}$
$\frac{1}{2}x+y=\frac{-2}{6}$
$\frac{1}{2}x+y=\frac{-1}{3}$