Give a reason why L₁ does not pass through A.

Find the gradient of L₁.

L₂ is a line perpendicular to L₁. The equation of L₂ is \(y = mx + c\).

Write down the value of m.

L₂ does pass through A.

Find the value of c.

\(2 \times 0 - 3 \times 6 \ne 11\)     (R1)

Note: Stating \(2 \times 0 - 3 \times 6 =  - 18\) without a conclusion is not sufficient.

OR

Clear sketch of L₁ and A.

     (R1)

OR

Point A is (6, 0) and \(2y - 3x = 11\) has x-intercept at \(- \frac{11}{3}\) or the line has only one x-intercept which occurs when x is negative.     (R1)     (C1)

\(2y = 3x + 11\) or \(y - \frac{3}{2}x = \frac{{11}}{2}\)     (M1)

Note: Award (M1) for a correct first step in making y the subject of the equation.

\(({\text{gradient equals}}) = \frac{3}{2}(1.5)\)     (A1)     (C2)

Note: Do not accept 1.5x.

\((m = ) - \frac{2}{3}\)     (A1)(ft)     (C1)

Notes: Follow through from their part (b).

\(0 =  - \frac{2}{3}(6) + c\)     (M1)

Note: Award (M1) for correct substitution of their gradient and (6, 0) into any form of the equation.

(c =) 4     (A1)(ft)     (C2)

Note: Follow through from part (c).

There were multiple acceptable reasons why the line did not pass through a given point (including numerically substituting values in the equation; drawing a graph or algebraically finding the x-intercept of the line). This was one of two reasoning marks in the paper.

There were multiple acceptable reasons why the line did not pass through a given point (including numerically substituting values in the equation; drawing a graph or algebraically finding the x-intercept of the line). This was one of two reasoning marks in the paper.

There were multiple acceptable reasons why the line did not pass through a given point (including numerically substituting values in the equation; drawing a graph or algebraically finding the x-intercept of the line). This was one of two reasoning marks in the paper.

There were multiple acceptable reasons why the line did not pass through a given point (including numerically substituting values in the equation; drawing a graph or algebraically finding the x-intercept of the line). This was one of two reasoning marks in the paper.