Calculate the gradient of \(L\) .

Find the equation of \(L\) .

The line \(L\) also passes through the point \({\text{P}}(8{\text{, }}y)\) . Find the value of \(y\) .

\(\frac{{8 - 4}}{{5 - ( - 1)}}\)     (M1)

Note: Award (M1) for correct substitution into the gradient formula.

\(\frac{2}{3}{\text{ }}\left( {\frac{4}{6}{\text{, }}0.667} \right)\)     (A1)     (C2)

[2 marks]

\(y = \frac{2}{3}x + c\)     (A1)(ft)

Note: Award (A1)(ft) for their gradient substituted in their equation.

\(y = \frac{2}{3}x + \frac{{14}}{3}\)     (A1)(ft)     (C2)

Notes: Award (A1)(ft) for their correct equation. Accept any equivalent form. Accept decimal equivalents for coefficients to 3 sf.

OR

\(y - {y_1} = \frac{2}{3}(x - {x_1})\)     (A1)(ft)

Note: Award (A1)(ft) for their gradient substituted in the equation.

\(y - 4 = \frac{2}{3}(x + 1)\)     OR     \(y - 8 = \frac{2}{3}(x - 5)\)     (A1)(ft)     (C2)

Note: Award (A1)(ft) for correct equation.

[2 marks]

\(y = \frac{2}{3} \times 8 + \frac{{14}}{3}\)     OR     \(y - 4 = \frac{2}{3}(8 + 1)\)     OR     \(y - 8 = \frac{2}{3}(8 - 5)\)     (M1)

Note: Award (M1) for substitution of \(x = 8\) into their equation.

\(y = 10\) (\(10.0\))     (A1)(ft)     (C2)

Note: Follow through from their answer to part (b).

[2 marks]

Generally, a well answered question with many candidates achieving full marks. Indeed, marks which tended to be lost were as a result of premature rounding rather than method. On a number of scripts, part (a) produced a rather curious wrong answer of \(8.2\) following a correct gradient expression. It would seem that this was as a result of typing into the calculator \(8 - 4 ÷ 5 + 1\).

Generally, a well answered question with many candidates achieving full marks. Indeed, marks which tended to be lost were as a result of premature rounding rather than method.

Generally, a well answered question with many candidates achieving full marks. Indeed, marks which tended to be lost were as a result of premature rounding rather than method.