The equation of the line parallel to the given line that contains point $ A $ is:
$ \color{blue}{ x-2y+14=0 }$ ( General form )
$ \color{blue}{ y = \frac{ 1 }{ 2 } x + 7 } ~~~$ ( Slope y-intercept form )
Step 1:The slope of a given line is $ m = \frac{ 1 }{ 2 } $.
Step 2: Parallel lines have the same slope, so the slope of the unknown line ($ m_1 $) will also be $ \frac{ 1 }{ 2 } $. So the parallel line will have a slope of $ m_1 = \frac{ 1 }{ 2 } $
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 }{ 2 } $ , $ x_0 = -8 $ and $ y_0 = 3 $. After substitution we have:
$$ \begin{aligned} y - y_0 =& ~ m_1 (x - x_0) \\ y - 3 =& ~ \frac{ 1 }{ 2 } ( x - \left( -8\right)) \\y -3 =& ~ \frac{ 1 }{ 2 } x + 4 \\y =& ~ \frac{ 1 }{ 2 } x + 4 + 3 \\y =& ~ \frac{ 1 }{ 2 } x + 7\\ \end{aligned} $$