Defining features of linear relationships
I can appreciate that there are two key elements to any linear relationship: rate of change and intercept point.
Defining features of linear relationships
I can appreciate that there are two key elements to any linear relationship: rate of change and intercept point.
These resources will be removed by end of Summer Term 2025.
Lesson details
Key learning points
- There is always a common difference in an arithmetic sequence.
- There is always a constant rate of change on a linear graph.
- There is always an initial value in an arithmetic sequence.
- There is always an intercept point with the y-axis on a linear graph.
- These two features uniquely describe any linear relationship.
Keywords
Rate of change - The rate of change is how quickly one variable changes with respect to another. If constant, there is a linear relationship.
Intercept - An intercept is the coordinate where a line or curve meets a given axis.
Common misconception
The arithmetic sequence 5n+2 starts at 7 so the linear equation y=5x+2 'starts' somewhere.
y=5x+2 has no start and no end; it goes on infinitely. However, all linear equations have a y-intercept and this helps define them.
To help you plan your year 8 maths lesson on: Defining features of linear relationships, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 8 maths lesson on: Defining features of linear relationships, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
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The assessment exit quiz will test your pupils' understanding of the key learning points.
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Explore more key stage 3 maths lessons from the Graphical representations of linear equations unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Lesson video
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Starter quiz
6 Questions
$$11,4,-3,-10, ...$$ -
Starts at $$11$$ and decreases by $$7$$.
$$11,7,3,-1, ...$$ -
Starts at $$11$$ and decreases by $$4$$.
$$7,11,15,19, ...$$ -
Starts at $$7$$ and increases by $$4$$.
$$7,18,29,40, ...$$ -
Starts at $$7$$ and increases by $$11$$.
$$11,15,19,23, ...$$ -
Starts at $$11$$ and increases by $$4$$.
$$7,3,-1,-5, ...$$ -
Starts at $$7$$ and decreases by $$4$$.
$$-8,-3,2,7, ...$$ -
$$+5$$
$$7,2,-3,-8, ...$$ -
$$-5$$
$$-8,-6,-4,-2, ...$$ -
$$+2$$
$$-4,-6,-8,-10, ...$$ -
$$-2$$
$$4,1,-2,-5, ...$$ -
$$-3$$
$$-14,-11,-8,-5, ...$$ -
$$+3$$
Exit quiz
6 Questions
