## Calculus 10th Edition

$y=-\dfrac{x}{2}+5.$
$\dfrac{d}{dx}(x^{\frac{2}{3}})+\dfrac{d}{dx}(y^{\frac{2}{3}})=\dfrac{d}{dx}(5)\rightarrow$ $\dfrac{2}{3\sqrt[3]{x}}$+$\dfrac{dy}{dx}(\dfrac{2}{3\sqrt[3]{y}})=0\rightarrow$ $\dfrac{dy}{dx}=-\dfrac{\sqrt[3]{y}}{\sqrt[3]{x}}$ At $(8, 1)\rightarrow\dfrac{dy}{dx}=-\dfrac{\sqrt[3]{1}}{\sqrt[3]{8}}=-\dfrac{1}{2}.$ Equation of tangent: $(y-y_0)=m(x-x_0)$ at point $(x_0, y_0)$ and slope $m$. $(y-1)=-\dfrac{1}{2}(x-8)\rightarrow y=-\dfrac{x}{2}+5.$