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