2026 CSS P2 Q2

The equation of line \(L\) is \(3y=2x+9\).

The equation of line \(M\) is \(5y=kx+7\), where \(k\) is a constant.

Line \(L\) and line \(M\) intersect at the point \((3,p)\) where \(p\) is a constant.

Find the value of \(k\) and the value of \(p\).[3]

\(A\) is the point \((4,a)\) where \(a<0\). \(B\) is the point \((16,5)\).

The length of line \(AB\) is \(15\) units.

Find the value of \(a\).[3]