1 The points \(A\) and \(B\) have coordinates \(( 6 , - 1 )\) and \(( 2,5 )\) respectively.
- Show that the gradient of \(A B\) is \(- \frac { 3 } { 2 }\).
- Hence find an equation of the line \(A B\), giving your answer in the form \(a x + b y = c\), where \(a , b\) and \(c\) are integers.
- Find an equation of the line which passes through \(B\) and which is perpendicular to the line \(A B\).
- The point \(C\) has coordinates ( \(k , 7\) ) and angle \(A B C\) is a right angle.
Find the value of the constant \(k\).