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Year 8

Finding the equation of the line ay + bx + c = 0

I can appreciate that writing linear equations in the form ay + bx + c = 0 may be more appropriate.

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New
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Year 8

Finding the equation of the line ay + bx + c = 0

I can appreciate that writing linear equations in the form ay + bx + c = 0 may be more appropriate.

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. Linear equations can be written in multiple forms.
  2. One of these forms is ay + bx + c = 0.
  3. This form can be more appropriate in some contexts and situations.

Keywords

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

Common misconception

To draw the graph using the gradient and intercept you can just count the squares.

Encourage pupils to look at the scales on the axes carefully when drawing a line given the gradient and y-intercept.

Spotting the x- and y-intercept from ax+by+c=0 can lead to mistakes. Pupils should be substituting y=0 or x=0 and calculating rather than guessing. This is a tricky lesson, a recap on bar models may be useful prior to starting this lesson.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), 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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Starter quiz

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6 Questions

Q1.
The equation of this line is: $$y =$$ $$- 2x$$.
An image in a quiz
Correct Answer: 3
Q2.
This coordinate, ( , 0), lies on the line $$y + x = 4$$. What is the missing $$x$$ coordinate?
Correct Answer: 4
Q3.
This coordinate, ( , 0), lies on the line $$y + x = 7$$. What is the missing $$x$$ coordinate?
Correct Answer: 7
Q4.
Which of these coordinates lie on the $$x$$ axis?
Correct answer: (0,0)
(0,4)
Correct answer: (4,0)
(0, 0.3)
Correct answer: (0.9,0)
Q5.
Which of these equations could be represented by this bar model?
An image in a quiz
Correct answer: $$y = 5x - 8$$
Correct answer: $$ 5x = y + 8 $$
$$ y - 8 = 5x$$
$$8 + 5x = y$$
Correct answer: $$8 = 5x - y$$
Q6.
Which of these equations are written in the form $$y = mx + c$$ ?
$$y + x = 10$$
Correct answer: $$y = 5x + 1$$
$$x = 5$$
Correct answer: $$y = 7 - 3x$$
Correct answer: $$y = x$$

Exit quiz

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6 Questions

Q1.
The graph shows 5 lines labelled A, B, C, D and E. Match the lines to the equations.
An image in a quiz
Correct Answer:A (green),$$x = -4$$

$$x = -4$$

Correct Answer:B (blue),$$y = {1\over 3}x - 4$$

$$y = {1\over 3}x - 4$$

Correct Answer:C (black),$$y = -4 $$

$$y = -4 $$

Correct Answer:D (pink),$$y = {1\over 3}x + 4$$

$$y = {1\over 3}x + 4$$

Correct Answer:E (purple),$$y = -{1\over 3}x + 4$$

$$y = -{1\over 3}x + 4$$

Q2.
Which equations are represented in this bar model?
An image in a quiz
$$y= 2x - 4$$
$$2x + y + 4 = 0$$
Correct answer: $$y = 2x + 4$$
$$y = 4 - 2x$$
Correct answer: $$2x + 4 - y = 0$$
Q3.
Which equations are represented in this bar model?
An image in a quiz
Correct answer: $$y = 4x - 2$$
$$4x- y + 2 = 0$$
$$y = 4x + 2$$
Correct answer: $$y - 4x + 2 = 0$$
Correct answer: $$4x - y - 2 = 0$$
Q4.
Match the $$y$$-intercepts to the correct graph in the form $$y + x + c = 0$$
Correct Answer:(0, -7),$$y + x + 7 = 0$$

$$y + x + 7 = 0$$

Correct Answer:(0, 7),$$ y + x - 7 = 0$$

$$ y + x - 7 = 0$$

Correct Answer:(0, -10),$$y - x + 10 = 0$$

$$y - x + 10 = 0$$

Correct Answer:(0, 10),$$y - x - 10 = 0 $$

$$y - x - 10 = 0 $$

Correct Answer:(0,1),$$y + x - 1 = 0$$

$$y + x - 1 = 0$$

Correct Answer:(0,-1),$$y - x + 1 = 0$$

$$y - x + 1 = 0$$

Q5.
Match the $$x$$-intercepts to the correct graph in the form $$y + x + c = 0$$
Correct Answer:(-3,0),$$y + x + 3 = 0$$

$$y + x + 3 = 0$$

Correct Answer:(3,0),$$ y + x - 3 = 0$$

$$ y + x - 3 = 0$$

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

$$y - x + 5 = 0$$

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

$$y + x + 5 = 0 $$

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

$$x + y - 4 = 0$$

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

$$x - y + 4 = 0$$

Q6.
Which of these are the correct $$x$$ and $$y$$-intercepts for the equation $$3x + y - 6 = 0$$ ?
(6,0) and (0,6)
(-6,0) and (0,-6)
(2,0) and (0,2)
Correct answer: (2,0) and (0,6)
(6,0) and (0,-2)