[tex]\bf x^2+y^2=20\implies 2x+2y\cfrac{dy}{dx}=0\implies x+y\cfrac{dy}{dx}=0\\\\\\ \cfrac{dy}{dx}=\cfrac{-x}{y}\\\\
-------------------------------\\\\
y'(-4,2)=\cfrac{-(-4)}{2}\implies y'(-4,2)=2\\\\
-------------------------------\\\\
y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-2=2(x-(-4))
\\
\left. \qquad \right. \uparrow\\
\textit{point-slope form}
\\\\\\
y-2=2(x+4)\implies y-2=2x+8\implies \boxed{y=2x+10}[/tex]
