The gradient is a measure of how steep a line is.

Positive rate of change from a graph

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

Defining features of linear relationships

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

How much the $$y$$ values change for every 1 increase in $$x$$

How much the $$x$$ values change for every 1 increase in $$y$$

How much the $$y$$ values change for every 1 decrease in $$x$$

How much the $$x$$ values change for every 1 decrease in $$y$$

Which of these best describes the gradient?

Which of these lines have a positive gradient?

Match the lines labelled A, B, C, D with the correct gradient.

The coordinate (0,0) can also be called the {{ }}.

What is the step on the $$x$$ axis of this graph?

What is the missing number in this table of values for the equation $$y=5x-3$$ ?

A drink is made from 3 litres of juice and 9 litres of soda. Use the ratio table to work out the amount of soda needed for 1 litre of juice.

What is the missing value in this ratio table?

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

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 +2 in $$x$$ there is a change of -5 in $$y$$

For every change of +3 in $$x$$ there is a change of -9 in $$y$$

A table of values is shown for the relationship $$y = 11 - 3x$$. Which of these is true for this relationship?

Positive rate of change from a graph

Lesson outcome