Consider the line y=7x-1 find the equation of the line that is perpendicular to this line and passes through the point (-5,6)

 
an equation for the line in point-slope form and general form is :
y = ax+b   a : slope  ; the Passing through (x' ; y')
y' = ax'+b 
y-y' =a(x-x')      and : x' =-5   y' =6
calculate a :
let :  y = ax+b (D)
   y=7x-1(D')
.(D) perpendicular to(D') : slope (D) × slope (D') = -1 

 slope (D') = 7
slop(D)×(7 = -1
slope (D) = -1/7
equation for the line    :   y-y' =a(x-x') 
y-6 =(-1/7) (x+5)

It might be a glitch in the system, but good job with all those points