Answer
a) $m=1$
b) $y=x-3$
Work Step by Step
We have: $4x^2+2y^2=12$
We differentiate both sides with respect to $x$.
$8x+4y \dfrac{dy}{dx}=0 \\ \dfrac{dy}{dx}=\dfrac{-2x}{y} $
a) The slope at $(1, -2)$ is: $m=\dfrac{-(2)(1)}{(-2)}=1$
b) The equation of a tangent line at $(1, -2)$ is:
$y-y_1=m(x-x_1)\\ y-(-2)=1(x-1)\\ y+2=x-1\\ y=x-3$
