restart;
with(plots):
# Warning, the name changecoords has been redefined
eq1:=y^3-y=x-2*x^3;

contourplot(lhs(eq1)-rhs(eq1),x=-2..2,y=-2..2,contours=[0]);

eq2:=subs(x=0.5,eq1);

solve(eq2,y);

x0:=0.5;
y0:=-.2695944364;


m:=(1-6*x0^2)/(3*y0^2-1);

line:=m*(x-x0)+y0;

P1:=contourplot(lhs(eq1)-rhs(eq1),x=-2..2,y=-2..2,contours=[0]):
P2:=plot(line,x=-2..2):
display(P1,P2);