The equation of the line perpendicular to the given line that contains point $ A $ is:
$ \color{blue}{ 3x+y+4=0 }$ ( General form )
$ \color{blue}{ y = - 3 x - 4 } ~~~$ ( Slope y-intercept form )
Step 1:The slope of a given line is $ m = \frac{ 1 }{ 3 } $.
Step 2: The perpendicular slope ($ m_1 $) is negative reciprocal of the slope $ m $.
$$ m_1 = - \frac{1}{m} = -\frac{ 1 }{ \frac{ 1 }{ 3 } } = -3 $$So the perpendicular 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 = 2 $. After substitution we have:
$$ \begin{aligned} y - y_0 =& ~ m_1 (x - x_0) \\ y - 2 =& ~ -3 ( x - \left( -2\right)) \\y -2 =& ~ -3 x -6 \\y =& ~ -3 x -6 + 2 \\y =& ~ - 3 x - 4\\ \end{aligned} $$