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Checking and securing plotting a relationship

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

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Lesson 4 of 15

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Year 8

Checking and securing plotting a relationship

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

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Lesson details

Key learning points

A relationship between two variables can be described using a rule.
This relationship can be used to generate coordinate pairs.
These pairs can be plotted on a graph.
The shape of the curve made will give information about the relationship between the points.
All the points on the curve satisfy the relationship.

Keywords

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

Common misconception

All graphs are linear and if graphs are not linear you join points with straight line segments.

Explore $$n+2, 2n$$ and $$x^2$$. "I see $$n$$ and 2; they must be similar" pupils think. Get them to compare numerically, then graphically.

Do a sorting activity for 'Linear' and 'Non-linear'. You could give them $$n^{th}$$ term expressions, ask them to generate the first five terms and sort. For a less confident class give the pupils the first five terms and ask them to sort.

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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).

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Prior knowledge starter quiz

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6 Questions

Q1.
In algebra, when we replace variables with values we call this .

transforming

Correct answer: substituting

calculating

solving

Q2.
What is this coordinate?

$$(4,2)$$

Correct answer: $$(2,4)$$

$$2,4$$

$$4,2$$

Q3.
Which statements are true of this coordinate?

Correct answer: The $$y$$-coordinate is double the $$x$$-coordinate.

The $$y$$-coordinate is half the $$x$$-coordinate.

Correct answer: The $$y$$-coordinate is $$2$$ more than the $$x$$-coordinate.

The $$y$$-coordinate is $$2$$ more than the $$x$$-coordinate.

The $$x$$-coordinate and $$y$$-coordinate sum to $$4$$.

Q4.
What is the value of the expression $$5x-1$$ when $$x=3$$?

Correct Answer: 14, fourteen, Fourteen

Q5.
What is the value of the expression $$5x-1$$ when $$x=-3$$?

Correct answer: $$-16$$

$$-14$$

$$14$$

$$16$$

Q6.
Starting with the lowest, order the value of these expressions when $$x=2$$.

1 - $$4x-5$$

2 - $$10-3x$$

3 - $$7-x$$

4 - $$3x$$

5 - $$x+5$$

Assessment exit quiz

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6 Questions

Q1.
All of these coordinates fit the relationship $$x+y=5$$. This is an example of a relationship.

quadratic

Correct answer: linear

diagonal

constant

Q2.
What is the relationship between the $$x$$ and $$y$$ coordinates for the set $$(-1,-2)$$, $$(0,0)$$, and $$(1,2)$$?

$$x$$ is always $$1$$ away from $$y$$.

$$x$$ is always $$1$$ more than $$y$$.

$$x$$ is double $$y$$.

Correct answer: $$y$$ is double $$x$$.

Q3.
If we plot these coordinates will we see a linear relationship? $$(0,3)$$, $$(1,4)$$, $$(2,5)$$, $$(3,7)$$, and $$(4,7)$$.

Yes. This is an increasing linear relationship.

Correct answer: No. They do not fit the same rule.

It's impossible to know until we plot them.

Q4.
Match the coordinates to the respective rule.

Correct Answer:$$(1,5)$$,$$y=3x+2$$

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

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

Correct Answer:$$(3,5)$$,$$y=2x-1$$

Q5.
These coordinates all fit the relationship $$y=2x^2$$. Which words describe this relationship?

Linear

Correct answer: Non-linear

Straight line

Correct answer: Curve

Q6.
Some pupils are sharing $$36$$ sweets. As the number of pupils ($$p$$) varies, the numbers of sweets ($$s$$) each student gets varies. Which of the below represents this relationship?

$${p\over 36}=s$$

Correct answer: $${36\over p}=s$$

$${s\over 36}=p$$

$$p=36s$$

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UnitMaths / Graphical representations of linear equations

Maths

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Checking and securing plotting a relationship

Checking and securing plotting a relationship

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Equipment

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.In algebra, when we replace variables with values we call this .

Q2.What is this coordinate?

Q3.Which statements are true of this coordinate?

Q4.What is the value of the expression $$5x-1$$ when $$x=3$$?

Q5.What is the value of the expression $$5x-1$$ when $$x=-3$$?

Q6.Starting with the lowest, order the value of these expressions when $$x=2$$.

Assessment exit quiz

6 Questions

Q1.All of these coordinates fit the relationship $$x+y=5$$. This is an example of a relationship.

Q2.What is the relationship between the $$x$$ and $$y$$ coordinates for the set $$(-1,-2)$$, $$(0,0)$$, and $$(1,2)$$?

Q3.If we plot these coordinates will we see a linear relationship? $$(0,3)$$, $$(1,4)$$, $$(2,5)$$, $$(3,7)$$, and $$(4,7)$$.

Q4.Match the coordinates to the respective rule.

Q5.These coordinates all fit the relationship $$y=2x^2$$. Which words describe this relationship?

Q6.Some pupils are sharing $$36$$ sweets. As the number of pupils ($$p$$) varies, the numbers of sweets ($$s$$) each student gets varies. Which of the below represents this relationship?

Lesson appears in

UnitMaths / Graphical representations of linear equations

Maths

Q1.
In algebra, when we replace variables with values we call this .

Q2.
What is this coordinate?

Q3.
Which statements are true of this coordinate?

Q4.
What is the value of the expression $$5x-1$$ when $$x=3$$?

Q5.
What is the value of the expression $$5x-1$$ when $$x=-3$$?

Q6.
Starting with the lowest, order the value of these expressions when $$x=2$$.

Q1.
All of these coordinates fit the relationship $$x+y=5$$. This is an example of a relationship.

Q2.
What is the relationship between the $$x$$ and $$y$$ coordinates for the set $$(-1,-2)$$, $$(0,0)$$, and $$(1,2)$$?

Q3.
If we plot these coordinates will we see a linear relationship? $$(0,3)$$, $$(1,4)$$, $$(2,5)$$, $$(3,7)$$, and $$(4,7)$$.

Q4.
Match the coordinates to the respective rule.

Q5.
These coordinates all fit the relationship $$y=2x^2$$. Which words describe this relationship?

Q6.
Some pupils are sharing $$36$$ sweets. As the number of pupils ($$p$$) varies, the numbers of sweets ($$s$$) each student gets varies. Which of the below represents this relationship?