impl2parm := proc(impl_line)
   local a, b, c;
   a := coeff(impl_line, x);
   b := coeff(impl_line, y);
   c := subs({x=0,y=0}, impl_line);
   if(b = 0) then RETURN([-c/a, t]);
     else RETURN([t, -a/b*t-c/b]);
   fi;
end;

parm2impl := proc(parm_line)
   local xt, yt, x1, y1, x2, y2;
   xt := op(1, parm_line);
   yt := op(2, parm_line);
   x1 := subs(t=0, xt); x2 := subs(t=1, xt);
   y1 := subs(t=0, yt); y2 := subs(t=1, yt);
   expand((x2-x1)*(y-y1)-(y2-y1)*(x-x1));
end;