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Lesson 7 of 11
  • Year 10
  • Higher

Identifying perpendicular linear graphs

I can identify, from their equations or graphs, whether two lines are perpendicular.

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View unit
Lesson 7 of 11
New
New
  • Year 10
  • Higher

Identifying perpendicular linear graphs

I can identify, from their equations or graphs, whether two lines are perpendicular.

Download all resources
Share activities with pupils

These resources will be removed by end of Summer Term 2025.

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These resources were created for remote use during the pandemic and are not designed for classroom teaching.

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Lesson details

Key learning points

  1. If two equations are written in the form y = mx + c then you can identify if they are perpendicular.
  2. If the equations are not in that form, you can rearrange them to be.
  3. From their graphs, you can identify whether two lines are perpendicular.

Keywords

  • Perpendicular - Two lines are perpendicular if they meet at right angles.

  • Irrational number - An irrational number is one that cannot be written in the form a/b where a and b are integers and b is not equal to 0

  • Surd - A surd is an irrational number expressed as the root of a rational number.

  • Radical - The root sign is the radical symbol.

Common misconception

The gradients of two perpendicular lines are a number and its reciprocal.

In order for two lines to be perpendicular, the two gradients cannot have the same sign. Therefore it is a number and its negative reciprocal.


To help you plan your year 10 maths lesson on: Identifying perpendicular linear graphs, download all teaching resources for free and adapt to suit your pupils' needs...

Pupils may struggle to remember the relationship. Encourage them to sketch the graphs for their equations as a visual check for their working.
Teacher tip

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Prior knowledge starter quiz

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6 Questions

Q1.
Which of these show two lines which are perpendicular?

Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz

Q2.
What is the gradient of this line?

An image in a quiz
$$1\over 3$$
Correct answer: $$2\over 5$$
$$2\over 3$$
$$3\over 2$$
$$5\over 2$$

Q3.
Which of these values is the reciprocal of 4?

$$-4$$
Correct answer: $$1\over 4$$
$$0.4$$
$$2$$
$$10\over 4$$

Q4.
Which of these coordinates lie on the line $$x = 4.5$$?

(0, 0)
(2.5, 4.5)
(3, 1.5)
Correct answer: (4.5, 7)
(5, -0.5)

Q5.
Which of these lines are parallel to the line with equation $$2y-x = 5$$?

Correct answer: $$4y - 2x = 5$$
$$y = 2x + 8$$
Correct answer: $$y = {1\over 2}x - 1$$
$$y = 10-{1\over 2}x$$
$$6y - 4x = 3$$

Q6.
A line has gradient 4 and passes through the coordinate (3, 9). What is the equation of the line?

$$y = 21 - 4x$$
$$ y = 3x$$
Correct answer: $$ y = 4x - 3$$
$$ y = 4x$$
$$ y = 4x + 9$$

Assessment exit quiz

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6 Questions

Q1.
Match each number to its negative reciprocal.

Correct Answer:$$-3$$,$$1\over 3$$

$$1\over 3$$

Correct Answer:$$1$$,$$-1$$

$$-1$$

Correct Answer:$$7$$,$$-{1\over 7}$$

$$-{1\over 7}$$

Correct Answer:$$-{4\over 5}$$,$$5\over 4$$

$$5\over 4$$

Correct Answer:$$-{5\over 4}$$,$$4\over 5$$

$$4\over 5$$

Correct Answer:$$1\over 7$$,$$-7$$

$$-7$$

Q2.
Select the equation of a line perpendicular to the line with equation $$ y = {1\over 2}x$$.

$$ y = {1\over 4} x$$
$$ y = 5 - {1\over 2}x$$
$$y = {1\over 2}x + 4$$
$$ y = 2x + 1$$
Correct answer: $$ y = 4 - 2x$$

Q3.
Which of these are equations of a line perpendicular to the line with equation $$ 3y = 2x + 6$$?

$$ y = {2\over 3}x +1$$
$$ y =2 + {3\over 2}x $$
$$ y = 3 - {1\over 2}x $$
Correct answer: $$ y = 4 - {3\over 2}x $$
$$ y = {1\over 2}x + 5$$

Q4.
Which of these are equations for lines which are perpendicular to the line with equation $$y + 2.5x = 0$$?

Correct answer: $$y = {2\over 5}x +3$$
$$y = 3 - {5\over 2}x $$
$$ y = 5.2x + 3$$
$$2y + 5x = 3$$
Correct answer: $$5y = 2x + 3$$

Q5.
Which is the equation of the line which passes through the point (3, -1) and is perpendicular to the line with equation $$y =2-{1\over 3}x$$?

$$y = -3x + 8$$
$$y = {1\over 3}x -2$$
$$y = {1\over 3}x -4$$
$$y = 3x - 4$$
Correct answer: $$y = 3x - 10$$

Q6.
Which of these are equations for lines which are perpendicular to the line with equation $$y = {1\over\sqrt{20}}x$$?

$$y = 4 + \sqrt{20}x$$
Correct answer: $$y = 4 - \sqrt{20}x$$
$$ y = 4\sqrt{5} x + 4$$
Correct answer: $$ y = 4-2\sqrt{5} x$$
$$ y = 4-4\sqrt{5} x$$