Combine an algebraic range with an intersecting line

The curve $C$ has equation $y=\dfrac{x^2+3x-1}{x-2}$, $x\in\mathbb R$, $x\ne2$.

(i) Using an algebraic method, find the range of values that $y$ can take.

(ii) Sketch $C$, stating the equations of the asymptotes, axial intercepts and the coordinates of the turning points, if any.

(iii) State the range of values that $m$ can take such that the equation $\dfrac{x^2+3x-1}{x-2}=m(x-2)+7$ has 2 distinct solutions, justifying your answer.