Answer
$y+6=\dfrac{1}{5}(x+1)$
Work Step by Step
Using the properties of equality, the given linear equation, $
x-5y=1
$ is equivalent to
\begin{array}{l}
-5y=-x+1
\\\\
y=\dfrac{-1}{-5}x+\dfrac{1}{-5}
\\\\
y=\dfrac{1}{5}x-\dfrac{1}{5}
.\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{1}{5}
$. Since parallel lines have the same slope, then the needed linear equation has the same slope and it passes through the given point $(
-1,-6
)$. 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-(-6)=\dfrac{1}{5}(x-(-1))
\\\\
y+6=\dfrac{1}{5}(x+1)
.\end{array}
