Question

Find parametric equations of the line that is tangent to the parabola y = x^2 at the point (−2, 4).

Answer 1

dy/dx = 2x
so at (-2,4) slope is -4

y-4 = -4(x+2)
y-4 = -4x - 8 = k

-4x-8 = k
-4x = k + 8

x = -2 - k/4
y = 4 + k

Parametric equations for linear function ??
Why not just
y = -4x -4 ??