7. The curve \(C\) has equation
$$y = \frac { 1 } { 2 - x }$$
- Sketch the graph of \(C\). On your sketch you should show the coordinates of any points of intersection with the coordinate axes and state clearly the equations of any asymptotes.
The line \(l\) has equation \(y = 4 x + k\), where \(k\) is a constant.
Given that \(l\) meets \(C\) at two distinct points,
- show that
$$k ^ { 2 } + 16 k + 48 > 0$$
- Hence find the range of possible values for \(k\).