Answer
$y=-x+7.$
Work Step by Step
$\dfrac{d}{dx}((y-3)^2)=\dfrac{d}{dx}(4(x-5))\rightarrow$
$\dfrac{dy}{dx}(2(y-3))=4\rightarrow$
$\dfrac{dy}{dx}=\dfrac{2}{y-3}.$
At $(6, 1)\rightarrow\dfrac{dy}{dx}=\dfrac{2}{1-3}=-1.$
Equation of tangent:
$(y-y_0)=m(x-x_0)$ at point $(x_0, y_0)$ and slope $m$.
$(y-1)=-1(x-6)\rightarrow y=-x+7.$
