The rate of change is how quickly one variable changes with respect to another. If constant, there is a linear relationship.

An intercept is the coordinate where a line or curve meets a given axis.

Defining features of linear relationships

Maths

In this unit, pupils saw that an arithmetic sequence can be represented graphically and that this is a linear relationship. Any point on the line satisfies this relationship. In the future unit, pupils learn how to find a value that satisfies the relationship when the second value is known, without the aid of the graph.

The sequences unit allowed pupils to explore different ways of generating sequences and then representing an arithmetic sequence graphically. This served as an introduction to this unit on graphical representations of linear equations.

Graphical representations of linear equations

The {{ }} is how quickly one variable changes with respect to another. If the change is constant, there is a linear relationship between the variables.

For every change of $$+1$$ in $$x$$ there is a change of $$-2$$ in $$y$$.

For every change of $$+1$$ in $$x$$ there is a change of $$+2$$ in $$y$$.

For every change of $$+1$$ in $$y$$ there is a change of $$+2$$ in $$x$$.

For every change of $$+2$$ in $$x$$ there is a change of $$+4$$ in $$y$$.

Here is a table of values for the relationship $$y=2x-3$$. Which statements are true of the rate of change between the two variables?

For every change of $$+1$$ in $$x$$ there is a change of $$+3$$ in $$y$$.

For every change of $$+1$$ in $$y$$ there is a change of $$+3$$ in $$x$$.

For every change of $$+1$$ in $$x$$ there is a change of $$-3$$ in $$y$$.

For every change of $$+1$$ in $$y$$ there is a change of $$-3$$ in $$x$$.

What constant rate of change is shown by this linear graph?

An {{ }} is the coordinate where a line or curve meets a given axis.

What is the $$y$$-intercept of this line?

Starts at $$4$$ and has a rate of change of $$-2$$

Starts at $$2$$ and has a rate of change of $$+2$$

$$y$$-intercept at $$(4,0)$$ and has a rate of change of $$+2$$

$$y$$-intercept at $$(0,4)$$ and has a rate of change of $$-2$$

Which unique statement describes this line?

Two variables that change together at a constant rate when plotted on a graph will form a {{ }} relationship.

Match the arithmetic sequences to the descriptors.

Match the common differences to the arithmetic sequences.

Which of the below coordinates can you see plotted here?

Here is an arithmetic (linear) sequence for which we are given the second and fourth terms. Which of the below are the missing terms?

For the linear relationship $$y=15-7x$$ what is the $$y$$ coordinate when the $$x$$ coordinate is $$1.5$$? State your answer as a decimal.

This lesson will be removed by end of Summer Term 2025.

Defining features of linear relationships

Lesson outcome

This lesson will be removed by end of Summer Term 2025.