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.