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Plotting a relationship

Lesson details

Learning outcome

I can use a graphical representation to show all of the points (within a range) that satisfy a relationship.

Key learning points

  1. A line can be drawn using coordinates found following a rule.
  2. You can check any point on the line and it will satisfy the rule.
  3. Points that are not on the line do not satisfy the rule.
  4. Points can be tested to see if they are on the line or not.

Keywords

  • Substitution - Substitute means to put in place of another. In Algebra, substitution can be used to replace variables with values.

  • Integer - An integer is any positive or negative whole number or zero.

Common misconception

Pupils may join up their coordinates but not extend their line.

Lines are used to represent all coordinates that follow a rule. Unless given restrictions, lines should be infinitely long.

Teacher tip

You may wish to use substituting into trickier equations of lines as an opportunity to check calculator skills. Encourage the use of brackets around the x value being substituted and the arrow keys to easily change the value being substituted in.

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.
Write the coordinate of the point plotted on the graph shown

An image in a quiz
Correct Answer: (-1.5,-2.5)

Q2.
Which of these follow the rule $$y=8$$?

Correct answer: (-8,8)
(-8,-8)
(8,0)
Correct answer: (1.02,8)
(-5.6, 8.1)

Q3.
To __________ is to put in place of another. In algebra this can mean replacing variables with values.

change
generalise
plot
Correct answer: substitute
unitise

Q4.
Match the coordinate with the missing value so that each coordinate satisfies the rule $$y=-4x$$

Correct Answer:(3,____),-12

-12

Correct Answer:(-3,____),12

12

Correct Answer:(____,0),0

0

Correct Answer:(1,____),-4

-4

Correct Answer:(____, -16),4

4

Correct Answer:(____,4),-1

-1

Q5.
What is the value of the expression $$2x+5$$ when $$x=7$$?

Correct Answer: 19, nineteen

Q6.
What is the value of the expression $$10-5x$$ when $$x=-3$$

Correct Answer: 25, twenty-five, twenty five

6 Questions

Q1.
What is the minimum number of coordinates you need to plot to draw a straight line?

Correct Answer: 2, two

Q2.
Which of these is the correct way to draw the line of the rule $$y=2$$?

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

Q3.
True or false: The coordinate (5,9) will lie on the line $$y=x+4$$

Correct answer: True- The $$y$$ coordinate equals the $$x$$ coordinate plus 4
False- The $$x$$ coordinate equals the $$y$$ coordinate plus 4
There is no way of knowing without drawing the line

Q4.
Match the coordinate with the equation for the line it will lie on

Correct Answer:(3,6),$$y=x+3$$

$$y=x+3$$

Correct Answer:(-3,6),$$y=-2x$$

$$y=-2x$$

Correct Answer:(5,10),$$y=3x-5$$

$$y=3x-5$$

Correct Answer:(2,7),$$y=5x-3$$

$$y=5x-3$$

Q5.
Fill in the missing $$y$$ coordinate so this coordinate lies on the line $$y={1\over 2}x+4$$ (8, )

Correct Answer: 8

Q6.
Fill in the missing $$y$$ coordinate so this coordinate lies on the line $$y=-7x-15$$ (-3, )

Correct Answer: 6

To help you plan your 7 maths lesson on: Plotting a relationship, download all teaching resources for free and adapt to suit your pupils' needs...