[tex]\bf x^2+2xy-y^2+x=2\qquad
\begin{array}{llll}
(1&,&2)\\
x_1&&y_1
\end{array}\\\\
-------------------------------\\\\
2x+2\left( 1\cdot y+x\frac{dy}{dx} \right)-2y\frac{dy}{dx}+1=0
\\\\\\
2x+2y+2x\frac{dy}{dx}-2y\frac{dy}{dx}+1=0
\\\\\\
\cfrac{dy}{dx}(2x-2y)=-1-2x-2y\implies \cfrac{dy}{dx}=\cfrac{-1-2x-2y}{2x-2y}
\\\\\\
\left. \cfrac{dy}{dx}=\cfrac{2x+2y+1}{2y-2x} \right|_{1,2}\implies \cfrac{2+4+1}{4-2}\implies \cfrac{7}{2}\\\\
-------------------------------\\\\
[/tex]
[tex]\bf y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-2=\cfrac{7}{2}(x-1)\implies y-2=\cfrac{7}{2}x-\cfrac{7}{2}
\\
\left. \qquad \right. \uparrow\\
\textit{point-slope form}
\\\\\\
\boxed{y=\cfrac{7}{2}x-\cfrac{3}{2}}[/tex]
