Find the equation of the tangent to the curve \(y = 7 + 6 x - x ^ { 2 }\) at the point \(P\) where \(x = 5\), giving your answer in the form \(a x + b y + c = 0\).
This tangent meets the \(x\)-axis at \(Q\). Find the coordinates of the mid-point of \(P Q\).
Find the equation of the line of symmetry of the curve \(y = 7 + 6 x - x ^ { 2 }\).
State the set of values of \(x\) for which \(7 + 6 x - x ^ { 2 }\) is an increasing function.