Find the gradient of the line $L$.

Find the equation of the line $L$ in the form $y = ax + b$.

Write down a vector equation for the line $L$.

attempt to find gradient     (M1)

eg     reference to change in $x$ is $3$ and/or $y$ is $2$, $\frac{3}{2}$

gradient $= \frac{2}{3}$     A1     N2

[2 marks]

attempt to substitute coordinates and/or gradient into Cartesian equation

for a line     (M1)

eg     $y - 4 = m(x - 9),{\text{ }}y = \frac{2}{3}x + b,{\text{ }}9 = a(4) + c$

correct substitution     (A1)

eg     $4 = \frac{2}{3}(9) + c,{\text{ }}y - 4 = \frac{2}{3}(x - 9)$

$y = \frac{2}{3}x - 2{\text{   }}\left( {{\text{accept }}a = \frac{2}{3},{\text{ }}b =  - 2} \right)$     A1     N2

[3 marks]

any correct equation in the form r = a + tb (any parameter for t), where a indicates position eg $\left( \begin{array}{l}9\\4\end{array} \right)$ or $\left( \begin{array}{c}0\\ - 2\end{array} \right)$, and b is a scalar multiple of $\left( \begin{array}{l}3\\2\end{array} \right)$

eg r = $\left( \begin{array}{c}9\\4\end{array} \right) + t\left( \begin{array}{c}3\\2\end{array} \right),\left( \begin{array}{c}x\\y\end{array} \right) = \left( \begin{array}{c}3t + 9\\2t + 4\end{array} \right)$, r = 0i − 2 j + s(3i + 2 j)     A2     N2

Note: Award A1 for a + tb, A1 for L = a + tb, A0 for r = b + ta.

[2 marks]