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

Checking and securing understanding of plotting coordinates

Checking and securing understanding of plotting coordinates generated from a rule

Checking and securing understanding of plotting coordinates with technology

Checking and securing plotting a relationship

Features of linear relationships

Positive rate of change from a graph

Negative rate of change from a graph

Rate of change from a coordinate pair

The intercept point

The equation of a straight line

Finding the equation of the line y = mx + c

Finding the equation of the line ay + bx + c = 0

Using dynamic software to explore linear relationships

Problem solving with graphing linear relationships

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.

In this unti we develop understanding of linear relationships and explore the key features of a linear equation such as the gradient, intercept and determining an equation from coordinate pairs.

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.

Defining features of linear relationships

Lesson outcome