Write down the y intercept of L₁.

Write down the gradient of L₁.

The line L₂ is perpendicular to L₁ and passes through the point (3, 7).

Write down the gradient of the line L₂.

The line L₂ is perpendicular to L₁ and passes through the point (3, 7).

Find the equation of L₂. Give your answer in the form ax + by + d = 0 where \(a,{\text{ }}b,{\text{ }}d \in \mathbb{Z}\).

–2     (A1)     (C1)

Note: Accept (0, –2).

[1 mark]

\( - \frac{1}{2}\)     (A1)     (C1)

[1 mark]

2     (A1)(ft)     (C1)

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

[1 mark]

y = 2x + c (can be implied)
7 = 2 × 3 + c     (M1)
c = 1     (A1)(ft)
y = 2x + 1

Notes: Award (M1) for substitution of (3, 7), (A1)(ft) for c.

Follow through from their answer to part (c).

OR

y – 7 = 2(x – 3)     (M1)(M1)

Note: Award (M1) for substitution of their answer to part (c), (M1) for substitution of (3, 7).

2x – y + 1 = 0  or  –2x + y – 1 = 0     (A1)(ft)     (C3)

Note: Award (A1)(ft) for their equation in the stated form.

[3 marks]

Although the first three parts of this question were well answered, with most candidates knowing how to find the y intercept, gradient of a given line and gradient of the perpendicular line, very few candidates could find the equation of the perpendicular line and correctly state it in the required form.

Although the first three parts of this question were well answered, with most candidates knowing how to find the y intercept, gradient of a given line and gradient of the perpendicular line, very few candidates could find the equation of the perpendicular line and correctly state it in the required form.

Although the first three parts of this question were well answered, with most candidates knowing how to find the y intercept, gradient of a given line and gradient of the perpendicular line, very few candidates could find the equation of the perpendicular line and correctly state it in the required form.

Although the first three parts of this question were well answered, with most candidates knowing how to find the y intercept, gradient of a given line and gradient of the perpendicular line, very few candidates could find the equation of the perpendicular line and correctly state it in the required form.