The equation of the line parallel to the given line that contains point $ A $ is:
$ \color{blue}{ 3x-y-2=0 }$ ( General form )
$ \color{blue}{ y = 3 x - 2 } ~~~$ ( Slope y-intercept form )
Step 1:The slope of a given line is $ m = 3 $.
Step 2: Parallel lines have the same slope, so the slope of the unknown line ($ m_1 $) will also be $ 3 $. So the parallel line will have a slope of $ m_1 = 3 $
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 = 3 $ , $ x_0 = 2 $ and $ y_0 = 4 $. After substitution we have:
$$ \begin{aligned} y - y_0 =& ~ m_1 (x - x_0) \\ y - 4 =& ~ 3 ( x - 2) \\y -4 =& ~ 3 x -6 \\y =& ~ 3 x -6 + 4 \\y =& ~ 3 x - 2\\ \end{aligned} $$