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Year 8

The equation of a straight line

I can appreciate that writing linear equations in the form y = mx + c helps to reveal the structure.

icon-background-square
New
New
Year 8

The equation of a straight line

I can appreciate that writing linear equations in the form y = mx + c helps to reveal the structure.

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Lesson details

Key learning points

  1. Linear relationships can be written in a variety of algebraic forms.
  2. It is possible to identify the gradient and y-intercept when the equation is written in the form y=mx+c.
  3. The m comes from the French "monter" (to climb/ascend) and the c from "commencer" (to start).
  4. Linear equations can be rearranged in order to reveal the gradient and y-intercept.

Keywords

  • Equation of a line - Any equation whose graph forms a straight line.

  • Coefficient - A constant numerical multiplier of the variables in a term.

  • Constant - A term that does not change; it contains no variables.

Common misconception

Pupils may think graphs are only linear if written in the form y=mx+c

Use the first learning cycle as an opportunity to show graphs in many formats. y=mx+c makes the gradient and y intercept clear.


To help you plan your year 8 maths lesson on: The equation of a straight line, download all teaching resources for free and adapt to suit your pupils' needs...

The first learning cycle is a good chance to recap generating coordinates that fit a rule. For task A, pupils could write down as many coordinates as they can that satisfy the relationship before plotting.
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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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6 Questions

Q1.
Which equations are represented by the bar model shown?
An image in a quiz
Correct answer: $$a + 7 = 20$$
$$a + 20 = 7$$
$$7 = 20 + a $$
Correct answer: $$a = 20 - 7 $$
Correct answer: $$20 - a = 7$$
Q2.
Fill in the missing value for the $$y$$ intercept of this line $$(0,$$ $$)$$.
An image in a quiz
Correct Answer: -4
Q3.
Match up the coordinate with the relationship it satisfies.
Correct Answer:$$(5,1)$$,$$x + y = 6 $$
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$$x + y = 6 $$

Correct Answer:$$(-2,4)$$,$$ y = x + 6 $$
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$$ y = x + 6 $$

Correct Answer:$$(8,2)$$,$$x - y = 6$$
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$$x - y = 6$$

Correct Answer:$$(1,6)$$,$$2x + y = 8$$
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$$2x + y = 8$$

Correct Answer:$$(2,3)$$,$$x + 2y = 8 $$
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$$x + 2y = 8 $$

Correct Answer:$$(1,3)$$,$$ 2x + 2y = 8 $$
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$$ 2x + 2y = 8 $$

Q4.
What is the gradient of this line?
An image in a quiz
Correct Answer: 7
Q5.
Match up the expressions containing brackets with their expanded forms.
Correct Answer:$$6(x + 4)$$,$$6x + 24$$
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$$6x + 24$$

Correct Answer:$$6(2x + 4)$$,$$12x + 24$$
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$$12x + 24$$

Correct Answer:$$4(2x + 1)$$,$$8x + 4$$
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$$8x + 4$$

Correct Answer:$$4(x + 1)$$,$$4x + 4$$
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$$4x + 4$$

Correct Answer:$$2(3x + 2)$$,$$6x + 4$$
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$$6x + 4$$

Correct Answer:$$6(2x - 4)$$,$$12x - 24$$
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$$12x - 24$$

Q6.
Fill in this coordinate, $$(5,$$ $$)$$, so it satisfies the equation $$2x + 2y = 10$$.
Correct Answer: 0

6 Questions

Q1.
Match the keywords to their definitions.
Correct Answer:constant,a term that does not vary
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a term that does not vary

Correct Answer:coefficient,a numerical multiplier of a specific variable in a term
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a numerical multiplier of a specific variable in a term

Correct Answer:gradient,a measure of how steep a line is
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a measure of how steep a line is

Correct Answer:$$y$$-intercept,the coordinate where a line crosses the $$y$$ axis
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the coordinate where a line crosses the $$y$$ axis

Correct Answer:origin,the coordinate $$(0,0)$$
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the coordinate $$(0,0)$$

Correct Answer:equation of a straight line,a relationship which, when plotted, forms a straight line
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a relationship which, when plotted, forms a straight line

Q2.
Which of these relationships are represented by this bar model?
An image in a quiz
$$y - x = 5 $$
$$y + x = 5 $$
Correct answer: $$x - y = 5$$
Correct answer: $$x = y + 5$$
Correct answer: $$y = x - 5$$
Q3.
The graph shows 5 lines labelled A, B, C, D and E. Match the line to its gradient and $$y$$ intercept.
An image in a quiz
Correct Answer:A (purple),gradient $$1\over 2$$, $$y$$-intercept $$(0,-2)$$
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gradient $$1\over 2$$, $$y$$-intercept $$(0,-2)$$

Correct Answer:B (green),gradient $$1\over 2$$, $$y$$-intercept $$(0,2)$$
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gradient $$1\over 2$$, $$y$$-intercept $$(0,2)$$

Correct Answer:C (pink),gradient $$-2$$, $$y$$-intercept $$(0,-2)$$
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gradient $$-2$$, $$y$$-intercept $$(0,-2)$$

Correct Answer:D (blue),gradient $$-{1\over 2}$$, $$y$$-intercept $$(0,2)$$
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gradient $$-{1\over 2}$$, $$y$$-intercept $$(0,2)$$

Correct Answer:E (black),gradient $$2$$, $$y$$-intercept $$(0,-2)$$
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gradient $$2$$, $$y$$-intercept $$(0,-2)$$

Q4.
Match the equations of lines to their key features.
Correct Answer:$$y = 5x - 4$$,gradient $$5$$, $$y$$-intercept $$(0,-4)$$
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gradient $$5$$, $$y$$-intercept $$(0,-4)$$

Correct Answer:$$y = 4 - 5x$$,gradient $$-5$$, $$y$$-intercept $$(0,4)$$
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gradient $$-5$$, $$y$$-intercept $$(0,4)$$

Correct Answer:$$y = -4x - 5 $$,gradient $$-4$$, $$y$$-intercept $$(0,-5)$$
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gradient $$-4$$, $$y$$-intercept $$(0,-5)$$

Correct Answer:$$ y = 4x + 5 $$ ,gradient $$4$$, $$y$$-intercept $$(0,5)$$
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gradient $$4$$, $$y$$-intercept $$(0,5)$$

Correct Answer:$$y = 5x + 4$$,gradient $$5$$, $$y$$-intercept $$(0,4)$$
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gradient $$5$$, $$y$$-intercept $$(0,4)$$

Correct Answer:$$y = 5 - 4x $$,gradient $$-4$$, $$y$$-intercept $$(0,5)$$
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gradient $$-4$$, $$y$$-intercept $$(0,5)$$

Q5.
What are the key features of the graph with equation $$y= 3(5 - 2x)$$ ?
gradient $$15$$, $$y$$-intercept $$(0,-6)$$
gradient $$6$$, $$y$$-intercept $$(0,-15)$$
gradient $$-2$$, $$y$$-intercept $$(0,15)$$
gradient $$-2$$, $$y$$-intercept $$(0,5)$$
Correct answer: gradient $$-6$$, $$y$$-intercept $$(0,15)$$
Q6.
Which coordinates are on the line $$2x - y = 5$$ ?
Correct answer: $$(-2,-9)$$
$$(-1,3)$$
$$(0,5)$$
Correct answer: $$(7,9)$$
$$(10,5)$$