Answer
$y=3x-8$
Work Step by Step
In the form $y=mx+b,$ the given equation, $
3x-y=6
,$ is equivalent to
\begin{align*}
-y&=-3x+6
\\
(-1)(-y)&=(-3x+6)(-1)
\\
y&=3x-6
.\end{align*}
Using $y=mx+b$ or the Slope-Intercept Form of linear equations, where $m$ is the slope, the slope of the given line is $3$. Since parallel lines have the same slope (but different $y$-intercepts), the slope of the line parallel to the given line is $m=3$.
Using $y-y_1=m(x-x_1)$ or the Point-Slope Form of linear equations, with $m=3$ and $(x_1,y_1)=(0,-8)$ then
\begin{align*}\require{cancel}
y-(-8)&=3(x-0)
\\
y+8&=3x
\\
y&=3x-8
.\end{align*}
Hence, the equation of the line parallel to $3x-y=6$ and passing through $(0,-8)$ is $y=3x-8$.
