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