Choose exam board for KS4 Computer Science (GCSE)
Choose exam board for KS4 English
Choose exam board for KS4 French
Choose exam board for KS4 Geography
Choose exam board for KS4 German
Choose exam board for KS4 History
Choose tier for KS4 Maths
Choose exam board for KS4 Music
Choose exam board for KS4 Physical education (GCSE)
Choose exam board for KS4 Religious education (GCSE)
Choose exam board for KS4 Spanish

Finding the equation of the line y = mx + c

Lesson details

Learning outcome

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

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.

Teacher tip

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.

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

Loading...

Prior knowledge starter quiz

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: $$ y = -{1\over 2}x - 1$$
$$ y = -{1\over 2}x $$
$$ y = {1\over 2}x $$

To help you plan your 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...