Perform implicit differentiation.

x³ + x²y - y³ = -5

Differentiate with respect to x,

3x² + x² dy/dx + 2xy - 3y² dy/dx = 0

3x² + (x² - 3y²)dy/dx + 2xy = 0

(x² - 3y²)dy/dx = -2xy - 3x²

dy/dx = (-2xy - 3x²)/(x² - 3y²)

Sub x = 1, y = 2,

dy/dx = (-2(1)(2) - 3(1²)) / (1² - 3(2²)
= -7/-11
= 7/11


So gradient of the tangent at the point (1,2) is 7/11.

m = 7/11


Next, y = mx + c

sub x = 1, y = 2, m = 7/11,


2 = 7/11 (1) + c

c = 2 - 7/11 = 15/11

Oh i see! Thanks!

Welcome.

You may want to rewrite dy/dx = (-2xy - 3x²)/(x² - 3y²) as

dy/dx = (2xy + 3x²)/(3y² - x²) if you don't want 2 negatives in the numerator.

Ok got it