The equation of the line parallel to the given line that contains point $ A $ is:
$ \color{blue}{ x+5y+50=0 }$ ( General form )
$ \color{blue}{ y = - \frac{ 1 }{ 5 } x - 10 } ~~~$ ( Slope y-intercept form )
Step 1:The slope of a given line is $ m = -\frac{ 1 }{ 5 } $.
Step 2: Parallel lines have the same slope, so the slope of the unknown line ($ m_1 $) will also be $ -\frac{ 1 }{ 5 } $. So the parallel line will have a slope of $ m_1 = -\frac{ 1 }{ 5 } $
Step 3: Now we have a point and the slope so we can use point-slope form, which is:
$$ y - y_0 = m_1 (x - x_0) $$In this example we have: $ m_1 = -\frac{ 1 }{ 5 } $ , $ x_0 = -10 $ and $ y_0 = -8 $. After substitution we have:
$$ \begin{aligned} y - y_0 =& ~ m_1 (x - x_0) \\ y - \left( -8\right) =& ~ -\frac{ 1 }{ 5 } ( x - \left( -10\right)) \\y + 8 =& ~ -\frac{ 1 }{ 5 } x -2 \\y =& ~ -\frac{ 1 }{ 5 } x -2 -8 \\y =& ~ - \frac{ 1 }{ 5 } x - 10\\ \end{aligned} $$