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Different types of equations

Lesson details

Learning outcome

I can recognise that there are many different types of equations of which linear is one type.

Key learning points

  1. An equation is a statement that two expressions are equal, indicated by =.
  2. Linear expressions can be represented by a straight line on a graph.
  3. Non-linear expressions can be identified from their graphical form.
  4. Equations can be grouped as linear or non-linear.

Keywords

  • Gradient - The gradient is a measure of how steep a line is

  • Expression - Expressions contain one or more terms, where each term is separated by an operator.

  • Equation - An equation is used to show that one number or calculation is equal to another.

  • Linear - The relationship between two variables is linear if, when plotted on a pair of axes, a straight line is formed.

Common misconception

Pupils may think all equations are for straight lines so can be plotted from 2 points.

Explore different relationships, most relationships are not linear but we focus a lot on linear relationships and their unique structure.

Teacher tip

The use of graphing software will help pupils plot more complicated equations. This will then be useful when finding solutions to equations from graphs.

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

6 Questions

Q1.
Work out the value of $$(−4)^2$$.

−16
−8
−2
8
Correct answer: 16

Q2.
Which of these is the best description of the gradient of a line?

the $$x$$ value where the line crosses the $$x$$-axis
the length of the line
the thickness of the line
Correct answer: the steepness of the line
the vertical distance from the origin to the line

Q3.
Select the coordinates that lie on the line $$y = 2x − 3$$.

(−2, 1)
(0, 3)
Correct answer: (1, −1)
Correct answer: (4, 5)
(5, 4)

Q4.
The table shows values for the equation $$y = 5 − 3x$$. The missing number is .

An image in a quiz
Correct Answer: −1, negative 1, − 1, -1, - 1

Q5.
When the equation of a straight line is written in the form $$y = mx + c$$, ($$m$$) is the coefficient of $$x$$ and represents the .

Correct Answer: gradient

Q6.
Work out the value of $$y$$ that satisfies the equation $$3x + y = 6(x − 2)$$ when $$x = 5$$. $$y =$$

Correct Answer: 3

6 Questions

Q1.
Which of these equations are linear? The graphs of the equations are shown.

An image in a quiz
$$y = {3^2} − {4\over x}$$
Correct answer: $$y = {3^2} − {x\over 4}$$
$$y = {3^2} − 4x^2$$

Q2.
Which is the correct graph of the expression $$2 − 4t$$ as $$t$$ varies? The table of values for $$2 − 4t$$ is shown.

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

Q3.
The table of values for $$y = {30\over x}$$ is shown. The missing value is .

An image in a quiz
Correct Answer: 15

Q4.
Select the correct graph of the expression $$y = {x^3} − 5$$. The table of values for $$y = {x^3} − 5$$ is shown.

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

Q5.
The table of values for $$ 2x + y = 5(x − 1)$$ is shown. The missing value is .

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Correct Answer: 1

Q6.
The table of values for $$ xy = 12$$ is shown. The missing value is .

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Correct Answer: 6

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