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

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

The relationship between two variables is linear if, when plotted on a pair of axes, a straight line is formed.

The intercept point

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

Rate of change from a coordinate pair

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

What is the $$y$$-intercept for the line formed when this table of values is plotted?

Which of these coordinates could be a $$y$$-intercept?

The graph shows 5 lines labelled A, B, C, D, E. Match the line to its corresponding $$y$$ intercept.

What is the $$y$$ intercept for the line belonging to this table of values?

Match up the $$y$$-intercepts with the corresponding lines. 

A point on the line where the $$x$$ and $$y$$ coordinates are the same

A point on the line which you use to find the gradient. 

A point on the line where both values are positive.

A point on the line where it meets an axis.

Which of these best describes an intercept point?

The tables shown have been labeled A,B,C,D,E. Match the table with the correct gradient.

In a linear sequence the common difference is 3 and the tenth term is 32. What is the first term?

What is the gradient of the line which passes through the coordinates (4, 7) and (6,11) ?

What is the gradient of the line which passes through the coordinates (2, -6) and (0,-1) ?

Starter Quiz

Which of these sequences are linear?