8. The straight line \(l _ { 1 }\) has gradient \(\frac { 3 } { 2 }\) and passes through the point \(A ( 5,3 )\).
- Find an equation for \(l _ { 1 }\) in the form \(y = m x + c\).
The straight line \(l _ { 2 }\) has the equation \(3 x - 4 y + 3 = 0\) and intersects \(l _ { 1 }\) at the point \(B\).
- Find the coordinates of \(B\).
- Find the coordinates of the mid-point of \(A B\).
- Show that the straight line parallel to \(l _ { 2 }\) which passes through the mid-point of \(A B\) also passes through the origin.