xy³+0y+0.9=0, xy³+0.9=0 (red curve).
Differentiate wrt x: y³+3xy²(dy/dx)=0, 3xy²(dy/dx)=-y³, 3x(dy/dx)=-y, dy/dx=-y/(3x) for y≠0.
At (-0.9,1) dy/dx=(-1)/(3(-0.9))=1/2.7=10/27.
Equation of tangent (blue line):
y-1=(10/27)(x+0.9)=10x/27+⅓, y=10x/27+4/3.