SPS SPS SM 2025 October — Question 3

Exam BoardSPS
ModuleSPS SM (SPS SM)
Year2025
SessionOctober
TopicStraight Lines & Coordinate Geometry

3. The line \(l\) passes through the points \(A ( - 3,0 )\) and \(B \left( \frac { 5 } { 2 } , 22 \right)\)
  1. Find the equation of \(l\) giving your answer in the form \(y = m x + c\) where \(m\) and \(c\) are constants. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{2fa9e78c-8210-456c-9b70-5378609ac47d-04_728_959_447_625} \captionsetup{labelformat=empty} \caption{Figure 2}
    \end{figure} Figure 2 shows the line \(l\) and the curve \(C\), which intersect at \(A\) and \(B\).
    Given that
    • \(C\) has equation \(y = 2 x ^ { 2 } + 5 x - 3\)
    • the region \(R\), shown shaded in Figure 2, is bounded by \(l\) and \(C\)
    • use inequalities to define \(R\).
      (2)
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