8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{937246f9-2b6a-48df-b919-c6db3d6f863b-20_1063_1319_251_365}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 shows the straight line \(l _ { 1 }\) with equation \(4 y = 5 x + 12\)
- State the gradient of \(l _ { 1 }\)
The line \(l _ { 2 }\) is parallel to \(l _ { 1 }\) and passes through the point \(E ( 12,5 )\), as shown in Figure 2.
- Find the equation of \(l _ { 2 }\). Write your answer in the form \(y = m x + c\), where \(m\) and \(c\) are constants to be determined.
The line \(l _ { 2 }\) cuts the \(x\)-axis at the point \(C\) and the \(y\)-axis at the point \(B\).
- Find the coordinates of
- the point \(B\),
- the point \(C\).
The line \(l _ { 1 }\) cuts the \(y\)-axis at the point \(A\).
The point \(D\) lies on \(l _ { 1 }\) such that \(A B C D\) is a parallelogram, as shown in Figure 2.
- Find the area of \(A B C D\).