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Year 8

Finding the equation of the line y = mx + c

I can find the equation of the line in the form y = mx + c

icon-background-square
New
New
Year 8

Finding the equation of the line y = mx + c

I can find the equation of the line in the form y = mx + c

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Lesson details

Key learning points

  1. Linear equations can be rearranged into the form y =mx + c.
  2. The gradient and intercept can be identified from the graph.
  3. The equation of the line can be written in the form y = mx + c.

Keywords

  • Equation of a line - An equation of a line is any equation whose graph forms a straight line.

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

  • Intercept - An intercept is the coordinate where a line or curve meets a given axis.

Common misconception

Writing the gradient as the constant and the y intercept as the coefficient of x.

Link to linear sequences where the coefficient of n is the common difference in the sequence to help pupils see why (m) is the gradient.


To help you plan your year 8 maths lesson on: Finding the equation of the line y = mx + c, download all teaching resources for free and adapt to suit your pupils' needs...

This is a good opportunity to practise substitution skills. Pupils should be checking their equations by seeing if the coordinates satisfy the equation. A recap of substituting using a calculator may also be useful.
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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.
What is the $$y$$-intercept of the line with equation $$y = 5x - 1$$ ?
(0, -5)
Correct answer: (0, -1)
(0,1)
(0,5)
Q2.
What is the gradient of the line with equation $$y = x + 7$$ ?
Correct Answer: 1, one
Q3.
What is the gradient of this line?
An image in a quiz
Correct Answer: -5, negative five
Q4.
What is the value of the expression $$10 - 3x$$ when $$x=2$$ ?
Correct Answer: 4, four
Q5.
Which coordinates are on the line $$ y = 5x - 6 $$ ?
(10,4)
(2,16)
Correct answer: (1,-1)
Correct answer: (0, -6)
(-1, 1)
Q6.
What is the $$y$$-intercept for the line formed when these coordinates are plotted?
An image in a quiz
(0,-11)
(0, 5)
(0,7)
Correct answer: (0,19)
(0,20)

6 Questions

Q1.
Which of these is an equation for the line which has $$y$$-intercept (0,-4) and gradient 3?
$$y = -4x + 3$$
$$y = 3x + 4$$
$$y = 4 - 3x$$
Correct answer: $$y = 3x - 4$$
Q2.
Which of these is an equation for the line which has gradient -1 and $$y$$-intercept 5?
$$y = x - 5$$
Correct answer: $$y = 5 - x$$
$$y = 1 - 5x$$
$$y = 5x - 1$$
Q3.
The equation of this line is: $$y =$$ $$x - 1$$.
An image in a quiz
Correct Answer: 3
Q4.
The equation of the line formed by plotting these coordinates is: $$y =$$ $$- 2x$$.
An image in a quiz
Correct Answer: 6
Q5.
Which of these is the equation of this line?
An image in a quiz
$$ y = {1\over 3}x - 4$$
$$ y = -{1\over 3}x - 4$$
$$ y = 4 - 3x $$
Correct answer: $$ y = -3x - 4$$
$$ y = -2x - 4$$
Q6.
Which of these is the equation of the line joining the coordinates (-4,1) and (2,-2)? Use the broken table to help.
An image in a quiz
$$ y = -2x - 7$$
$$ y = -2x + 2$$
Correct answer: $$ y = -{1\over 2}x - 1$$
$$ y = -{1\over 2}x $$
$$ y = {1\over 2}x $$