Answer
a) $m=-2000$
b) $y=-2000x+6000$
Work Step by Step
We have: $xy-2000=y$
We differentiate both sides with respect to $x$.
$x \dfrac{dy}{dx}+y-0= \dfrac{dy}{dx}\\ \dfrac{dy}{dx}=\dfrac{y}{1-x}$
a) The slope at $(2, 2000)$ is: $m=\dfrac{2000}{1-2} = - 2000$
b) The equation of a tangent line at $(2, 2000)$ is:
$y-y_1=m(x-x_1)\\ y -2000=-2000(x-2) \\ y=-2000x+6000$
