Math (Calculus): By the way, I'm struggling to isolate y after plugging all values in the equation, "y=f'(x)(x-a) + f(a)"

Question

Question:

Find the equation of the tangent to the following equation, x³ - y³ = (x-2)y+1, at point (1.-1).

Answer: y=(3/2)x-(5/2)

Answer 1

x³ - y³ = (x-2)y + 1

Differentiate implicitly

3x² - 3y²y' = (x-2)y' + y

You actually don't have to solve algebraically for y' because you want it at (1,-1):

3 - 3y' = -y' -1 or -2y' = -4 y' = 2

which is a different slope than the equation given (my result is y+1 = 2(x-1) or y = 2x -3)

If you do it algebraically before substituting, group y' terms:

(-3y²-x+2)y^' = y-3x² or y' = (y-3x²)/(-3y²-x+2) (=2 at (1,-1))

I believe this is correct, so equation, point, or answer is incorrect.

Please consider a tutor. Take care.