Any one of the four areas into which a space is divided by the <i>x</i>- and <i>y</i>-axes in the Cartesian coordinate system.

Checking and securing understanding of plotting coordinates

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.

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

A sequence where the difference between successive terms is a constant.

Checking and securing understanding of plotting coordinates generated from a rule

Checking and securing understanding of plotting coordinates with technology

Substitute means to put in place of another.  In Algebra, substitution can be used to replace variables with values.

Checking and securing plotting a relationship

The relationship between two variables is linear when they change together at a constant rate and form a straight line when plotted.

Features of linear relationships

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

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

Positive rate of change from a graph

The absolute value of a number is its distance from zero.

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

Negative rate of change from a graph

Rate of change from a coordinate pair

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

The intercept point

Any equation whose graph forms a straight line.

A constant numerical multiplier of the variables in a term.

A term that does not change; it contains no variables.

The equation of a straight line

An equation of a line is any equation whose graph forms 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

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

Graphical representations of linear equations

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These lessons will be removed by end of Summer Term 2025.