9. The line \(L _ { 1 }\) has equation \(2 y - 3 x - k = 0\), where \(k\) is a constant.
Given that the point \(A ( 1,4 )\) lies on \(L _ { 1 }\), find
- the value of \(k\),
- the gradient of \(L _ { 1 }\).
The line \(L _ { 2 }\) passes through \(A\) and is perpendicular to \(L _ { 1 }\).
- Find an equation of \(L _ { 2 }\) giving your answer in the form \(a x + b y + c = 0\), where \(a\), \(b\) and \(c\) are integers.
The line \(L _ { 2 }\) crosses the \(x\)-axis at the point \(B\).
- Find the coordinates of \(B\).
- Find the exact length of \(A B\).