GCSE Maths · Higher · Chapter 10: Linear graphs · Lesson 2

Finding the equation of a line

Grades 5–8About 50 minutesNo calculator39 marks

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NameClassDate

Do Now

Grades 4–6

The first question is what today's lesson needs. The others bring back earlier topics.

A1
Needed today
Write down the gradient and the $y$ -intercept of $y = - x + 6$ .
[1 mark]
Answer
A2
From chapter 7
Triangles $A B C$ and $P QR$ are congruent, with $A$ matching $P$ , $B$ matching $Q$ and $C$ matching $R$ . Angle $A = 5 4^{\circ}$ and angle $B = 5 8^{\circ}$ . Find angle $R$ .
[1 mark]
Answer
A3
Key Stage 3
Three angles meet at a point. Two are $12 4^{\circ}$ and $12 1^{\circ}$ . Find the third.
[1 mark]
Answer
A4
Key Stage 3
Find the median of $2, 10, 24, 10, 5$ .
[1 mark]
Answer

Grades 5–6

Your teacher works through each example with you. Then try the one beside it.

Example 1

Work out the equation of the line through $(1, 5)$ and $(4, 17)$ .

Hint Find the gradient, then put one point into

y = m x + c

to find

c

B1
Work out the equation of the line through $(- 4, - 5)$ and $(2, 7)$ .
[3 marks]
Answer

Example 2

Work out the equation of the line perpendicular to $y = 2 x + 7$ that passes through $(4, 5)$ .

Hint Perpendicular gradients multiply to

- 1

B2
Work out the equation of the line perpendicular to $y = - 4 x + 1$ that passes through $(12, 5)$ .
[3 marks]
Answer

Grades 5–7

C1
Work out the equation of the line parallel to $y = 7 - 3 x$ that passes through $(2, 5)$ .
[2 marks]
Answer
C2
Are the lines $y = 2 x + 5$ and $2 y = 4 x - 1$ parallel? Give a reason.
[2 marks]

C3
Line $L$ has gradient $\frac{2}{5}$ . Write down the gradient of a line perpendicular to $L$ .
[1 mark]
Answer
C4
Work out the equation of the line shown.
[2 marks]
Answer
C5
A line has gradient $\frac{2}{3}$ and passes through $(- 2, 3)$ . Write its equation in the form $a x + b y = c$ , where $a$ , $b$ and $c$ are integers.
[3 marks]
Answer
C6
Show that the lines $5 x + 2 y = 9$ and $4 x - 10 y = 3$ are perpendicular.
[3 marks]

Grades 6–8

D1
Raj says, "The lines $y = 3 x + 1$ and $y = - 3 x + 4$ are perpendicular, because their gradients have opposite signs."
Explain why Raj is wrong.
[2 marks]

D2
$A$ is the point $(- 1, 4)$ and $B$ is the point $(4, 14)$ .
(a)
Work out the equation of the line through $A$ and $B$ .
[3 marks]
Answer
(b)
Line $M$ is perpendicular to $A B$ and passes through $B$ . Work out the coordinates of the point where $M$ crosses the $y$ -axis.
[3 marks]
Answer $(\dots\dots, \dots\dots)$
Total for D2: 6 marks
D3
The points $A (- 3, 2)$ and $B (5, 6)$ are shown on the grid. Work out the equation of the perpendicular bisector of $A B$ . Give your answer in the form $y = m x + c$ .
[4 marks]
Answer

Grade 8 and beyond

No route is given. The hints are at the end of the sheet. Use one at a time.

Colour one circle on each line.

	Not yet	Nearly	Yes
I can write the equation of a line from its graph or from two points.
I can find the equation of a line parallel or perpendicular to a given line, including a perpendicular bisector.

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