Question

Use the given conditions to write an equation for the line in​ point-slope form and general form.

Passing through (1,−7) and perpendicular to the line whose equation is x−2y−5=0

Answer 1

Hello there is solution :
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' =1 y' =-7
calculate a :
let : y = ax+b .....(D)
x-2y-5 =0 .....(D')
.(D) perpendicular to(D') : slope (D) × slope (D') = -1
but / x-2y-5 =0 .... 2y = x-5
y = (-1/2)x-5/2
slope (D') = -1/2
slop(D)×(-1/2) = -1
slope (D) = 2
equation for the line : y-y' =a(x-x')
y+7 =2 (x-1)
y = 2x-9