The line \(l _ { 1 }\) passes through the points \(P ( - 1,2 )\) and \(Q ( 11,8 )\).
Find an equation for \(l _ { 1 }\) in the form \(y = m x + c\), where \(m\) and \(c\) are constants.
The line \(l _ { 2 }\) passes through the point \(R ( 10,0 )\) and is perpendicular to \(l _ { 1 }\). The lines \(l _ { 1 }\) and \(l _ { 2 }\) intersect at the point \(S\).
Calculate the coordinates of \(S\).
Show that the length of \(R S\) is \(3 \sqrt { 5 }\).
Hence, or otherwise, find the exact area of triangle \(P Q R\).