Two lines are parallel if they are straight lines that are always the same (non-zero) distance apart.

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

Rate of change from a coordinate pair

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

Positive rate of change from a graph

Negative rate of change from a graph

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

Work out the gradient of the line which passes through (6,20) and (7,25).

Calculate the gradient of this line which goes through the origin.

A line with negative gradient is drawn through ( -4, 5) and one of these coordinates. Which coordinate could it be?

Work out the gradient of the line joining the coordinates (-5,11) and (-2,2).

Match the two coordinate pairs to the gradient of the line passing through them.

Which set of 3 coordinates lie on a straight line?

What is the missing number in this ratio table?

Match the points on the graph below with their corresponding coordinates.

Match the directed number calculations with the correct answer.

Which is the correct ratio table for the graph shown?

Rate of change from a coordinate pair

Lesson outcome