The equation of the line parallel to the given line that contains point $ A $ is:
$ \color{blue}{ 10x+y+106=0 }$ ( General form )
$ \color{blue}{ y = - 10 x - 106 } ~~~$ ( Slope y-intercept form )
Step 1:The slope of a given line is $ m = -10 $.
Step 2: Parallel lines have the same slope, so the slope of the unknown line ($ m_1 $) will also be $ -10 $. So the parallel line will have a slope of $ m_1 = -10 $
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 = -10 $ , $ x_0 = -10 $ and $ y_0 = -6 $. After substitution we have:
$$ \begin{aligned} y - y_0 =& ~ m_1 (x - x_0) \\ y - \left( -6\right) =& ~ -10 ( x - \left( -10\right)) \\y + 6 =& ~ -10 x -100 \\y =& ~ -10 x -100 -6 \\y =& ~ - 10 x - 106\\ \end{aligned} $$