Answer
$y=-\dfrac{4}{5}x+3$
Work Step by Step
Using the properties of equality, the given equation, $
5x-4y=10
,$ is equivalent to
\begin{array}{l}
-4y=-5x+10
\\\\
y=\dfrac{-5}{-4}x+\dfrac{10}{-4}
\\\\
y=\dfrac{5}{4}x-\dfrac{5}{2}
.\end{array}
Using $y=mx+b$, where $m$ is the slope, the slope is
\begin{array}{l}
m=\dfrac{5}{4}
.\end{array}
Using $m=
-\dfrac{4}{5}
$ (negative reciprocal since the lines are perpendicular) and the given point $(
-5,7
),$ then the equation of the line is
\begin{array}{l}
y-7=-\dfrac{4}{5}(x-(-5))
\\\\
y-7=-\dfrac{4}{5}(x+5)
\\\\
y-7=-\dfrac{4}{5}x-4
\\\\
y=-\dfrac{4}{5}x-4+7
\\\\
y=-\dfrac{4}{5}x+3
.\end{array}
