6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f39ade34-32e2-4b5c-b80a-9663c6a65c87-08_906_1100_127_388}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
The straight line \(l _ { 1 }\) has equation \(2 y = 3 x + 5\)
The line \(l _ { 1 }\) cuts the \(x\)-axis at the point \(A\), as shown in Figure 2.
- State the gradient of \(l _ { 1 }\)
- Write down the \(x\) coordinate of point \(A\).
Another straight line \(l _ { 2 }\) intersects \(l _ { 1 }\) at the point \(B\) with \(x\) coordinate 1 and crosses the \(x\)-axis at the point \(C\), as shown in Figure 2.
Given that \(l _ { 2 }\) is perpendicular to \(l _ { 1 }\)
- find an equation for \(l _ { 2 }\) in the form \(a x + b y + c = 0\), where \(a\), b and \(c\) are integers,
- find the exact area of triangle \(A B C\).