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.
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
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
