Answer
$y+4=\dfrac{5}{6}(x-3)$
Work Step by Step
Using the properties of equality, the given linear equation, $
5x-6y=4
$ is equivalent to
\begin{array}{l}
-6y=-5x+4
\\\\
y=\dfrac{-5}{-6}x+\dfrac{4}{-6}
\\\\
y=\dfrac{5}{6}x-\dfrac{2}{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 $
\dfrac{5}{6}
$. Since parallel lines have the same slope, then the needed linear equation has the same slope and it passes through the given point $(
3,-4
)$. 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, then the equation of the needed line is
\begin{array}{l}
y-(-4)=\dfrac{5}{6}(x-3)
\\\\
y+4=\dfrac{5}{6}(x-3)
.\end{array}
