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

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

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

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

Which of these graphs have a negative gradient?

Match the graphs to the correct gradient.

Starting with the steepest, put these gradients in order of steepness.

Which lines would be parallel to the one shown if drawn on the same axes?

rate of change in $$x$$ direction with respect to positive $$y$$ direction

rate of change in $$x$$ direction with respect to negative $$y$$ direction

rate of change in $$y$$ direction with respect to negative $$x$$ direction

rate of change in $$y$$ direction with respect to positive $$x$$ direction

Which of these is the correct explanation for how gradient is calculated?

Which of these tables of values show a relationship which will have a positive gradient when plotted?

Which is the correct ratio table for this graph?

Negative rate of change from a graph

Lesson outcome