Slope of Tangent Line through a Point with Implicit Differentiation (x^2y^2+5xy=14 at (2,1))

You can find the slope of the tangent through a point with implicit differentiation, which is what you'll need if you have y's scattered throughout the equation.
The SLOPE of the tangent is whatever y' (or dy/dx) ends up equalling when you fill in values for x and y themselves.