Answer
$\frac{dy}{dt}=\frac{10}{3}$
Work Step by Step
$y=\frac{9-4x}{3+2x}$
Find y value: $y=-7$
$3y+2xy=9-4x$
$3\frac{dy}{dt} + 2y\frac{dx}{dt}+2x\frac{dy}{dt}=-4\frac{dx}{dt}$
$(2x+3)\frac{dy}{dt}=(-2y-4))\frac{dx}{dt}$
Now substitute x=-3; y=-7; dx/dt=-1
$-3\frac{dy}{dt}=-10$
$\frac{dy}{dt}=\frac{10}{3}$
