關於Differentiation的簡單A.Maths.問題

Find the equations of the tangent and the normal to the given curve at the indicated point:

1. y = (x – 2)(x + 4); (-1, -9)

dy / dx = (x – 2)(1) + (x + 4)(1)
= 2x + 2

dy│
dx│(-1, -9) = 2(-1) + 2
= 0

∴ Equation of tangent:
y + 9 = 0(x + 1)
y = -9

∴ Equation of normal:
x + 1 = 0
x = -1

問題：為何equation of normal是這樣計算？答案及步驟是如何得來？