Answer
$\dfrac{10\sqrt 3}{9}$
Work Step by Step
Need to take the derivative of the given equations and then isolate the variables.
$ \dfrac{dx}{dt}=(\dfrac{-1}{2 \sqrt t})[\dfrac{1}{2 \sqrt {5-\sqrt t}}]$
$\implies \dfrac{\sqrt t}{t-1}+(t-1)\dfrac{dy}{dt}=\dfrac{1}{(2\sqrt t)}$
At $t=4$, we get
$ \dfrac{dx}{dt}=\dfrac{-1}{8\sqrt {3}}$ ;
and $ \dfrac{dy}{dt}=\dfrac{-5}{36}$
Hence, Slope: $\dfrac{dy}{dx}=\dfrac{-5/36}{-1/8\sqrt {3}}=\dfrac{10\sqrt 3}{9}$
