What is the slope of the line tangent to the graph of x^2xy+y^2=7?

Slope= $\frac{- 3 {x}^{2} y}{2 y + {x}^{3}}$
Differentiating the equation, it is ${x}^{3} \frac{\mathrm{dy}}{\mathrm{dx}} + 3 {x}^{2} y + 2 y \frac{\mathrm{dy}}{\mathrm{dx}} = 0$
$\left({x}^{3} + 2 y\right) \frac{\mathrm{dy}}{\mathrm{dx}} = - 3 {x}^{2} y$
$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{- 3 {x}^{2} y}{2 y + {x}^{3}}$