Answer
$\dfrac{-4}{5}$
Work Step by Step
Consider $\dfrac{dy}{dx}=-\dfrac{F_x}{F_y}$
Plug the derivatives in equation $\dfrac{dy}{dx}=-\dfrac{F_x}{F_y}$
This implies that $\dfrac{2x+y}{2y+x} \times (-1)=\dfrac{-(2x+y)}{2y+x}$
For the point $(1,2)$, we have
$\dfrac{-(2x+y)}{2y+x} =\dfrac{-(2+2)}{2(2)+1} =\dfrac{-4}{5}$
