7 Points \(A\) and \(B\) lie on the curve \(y = x ^ { 2 } - 4 x + 7\). Point \(A\) has coordinates \(( 4,7 )\) and \(B\) is the stationary point of the curve. The equation of a line \(L\) is \(y = m x - 2\), where \(m\) is a constant.
- In the case where \(L\) passes through the mid-point of \(A B\), find the value of \(m\).
- Find the set of values of \(m\) for which \(L\) does not meet the curve.