Answer
$y-6=-\dfrac{1}{4}(x+5)$
Work Step by Step
Using the properties of equality, the given linear equation, $
4x-y=3
$ is equivalent to
\begin{array}{l}
-y=-4x+3
\\\\
y=4x-3
.\end{array}
Using $y=mx+b$ or the Slope-Intercept form where $m$ is the slope, then the slope of the given line is $
4
$. Since perpendicular lines have negative reciprocal slopes, then the needed linear equation has slope equal to $
-\dfrac{1}{4}
$. Since it also passes through the given point $(
-5,6
)$, then using $y-y_1=m(x-x_1)$ or the Point-Slope form where $m$ is the slope and $(x_1,y_1)$ is a point on the line, the equation of the needed line is
\begin{array}{l}
y-6=-\dfrac{1}{4}(x-(-5))
\\\\
y-6=-\dfrac{1}{4}(x+5)
.\end{array}
