1 The point \(A\) has coordinates \(( 1,7 )\) and the point \(B\) has coordinates \(( 5,1 )\).
- Find the gradient of the line \(A B\).
- Hence, or otherwise, show that the line \(A B\) has equation \(3 x + 2 y = 17\).
- The line \(A B\) intersects the line with equation \(x - 4 y = 8\) at the point \(C\). Find the coordinates of \(C\).
- Find an equation of the line through \(A\) which is perpendicular to \(A B\).