10.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ce4f8375-0d88-4e48-85de-35f7e90b014d-20_643_767_276_648}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
The line \(l _ { 1 }\) has equation \(y = \frac { 3 } { 5 } x + 6\)
The line \(l _ { 2 }\) is perpendicular to \(l _ { 1 }\) and passes through the point \(B ( 8,0 )\), as shown in the sketch in Figure 4.
- Show that an equation for line \(l _ { 2 }\) is
$$5 x + 3 y = 40$$
Given that
- lines \(l _ { 1 }\) and \(l _ { 2 }\) intersect at the point \(C\)
- line \(l _ { 1 }\) crosses the \(x\)-axis at the point \(A\)
- find the exact area of triangle \(A B C\), giving your answer as a fully simplified fraction in the form \(\frac { p } { q }\)