6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ff1cdb91-0286-4bc8-9e67-451500b2bf74-07_647_927_274_513}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
The line \(l _ { 1 }\) has equation \(2 x - 3 y + 12 = 0\)
- Find the gradient of \(l _ { 1 }\).
The line \(l _ { 1 }\) crosses the \(x\)-axis at the point \(A\) and the \(y\)-axis at the point \(B\), as shown in Figure 1.
The line \(l _ { 2 }\) is perpendicular to \(l _ { 1 }\) and passes through \(B\).
- Find an equation of \(l _ { 2 }\).
The line \(l _ { 2 }\) crosses the \(x\)-axis at the point \(C\).
- Find the area of triangle \(A B C\).