8 A line has equation \(y = m x - 1\), where \(m\) is a constant.
A curve has equation \(y = x ^ { 2 } - 5 x + 3\).
- Show that the \(x\)-coordinate of any point of intersection of the line and the curve satisfies the equation
$$x ^ { 2 } - ( 5 + m ) x + 4 = 0$$
- Find the values of \(m\) for which the equation \(x ^ { 2 } - ( 5 + m ) x + 4 = 0\) has equal roots.
(4 marks) - Describe geometrically the situation when \(m\) takes either of the values found in part (b).
(1 mark)