Chapter 10 - Section 10.2 - Calculus with Parametric Curves - Exercises - Page 572: 20

$\dfrac{1}{2}$

Take the derivative of the given equations and isolate the variables. $2(x-t)=\dfrac{dx}{dt}$ and $\dfrac{dy}{dt}=e^t(t+1)$ At $t=0$, we have $x-t=1$ Then $ \dfrac{dx}{dt}=2$ At $t=1$, we have Then $ \dfrac{dx}{dt}=1$ Now, Slope: $\dfrac{dy}{dx}=\dfrac{1}{2}$