Answer
$-4$
Work Step by Step
Take the derivative of the given equations and isolate the variables.
$x \cos t+\sin t \dfrac{dx}{dt}+(2) \dfrac{dx}{dt}=1$
and $\dfrac{dy}{dt}=t\cos t+\sin t-2$
At $t=\pi$, we have $x=\pi/2$
Then $ \dfrac{dx}{dt}=2+\pi/4$
At $t=0$, we have
Then $ \dfrac{dx}{dt}=-\pi-2$
Now, Slope: $\dfrac{dy}{dx}=\dfrac{-\pi-2}{2+\pi/4}=-4$
