Question

find the equation of the tangent line to y^3-xy=-6 at the point (7,2)

Answer 1

Use implicit differentiation to find dy/dx as a function of x and y.

Evaluate dy/dx at (7,2) and use this as the slope m of a line that passes through the point (x1,y1):
(y-y1)=m(x-x1)
where (x1,y1)=(7,2)