An equation of a line is any equation whose graph forms a straight line.

Finding the equation of the line ay + bx + c = 0

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 intercept point

The equation of a straight line

Finding the equation of the line y = mx + c

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

The graph shows 5 lines labelled A, B, C, D and E. Match the lines to the equations.

Which equations are represented in this bar model?

Match the $$y$$-intercepts to the correct graph in the form $$y + x + c = 0$$

Match the $$x$$-intercepts to the correct graph in the form $$y + x + c = 0$$

Which of these are the correct $$x$$ and $$y$$-intercepts for the equation $$3x + y - 6 = 0$$ ?

The equation of this line is: $$y =$$ {{}} $$- 2x$$.

This coordinate, ({{ }}, 0), lies on the line $$y + x = 4$$. What is the missing $$x$$ coordinate?

This coordinate, ({{ }}, 0), lies on the line $$y + x = 7$$. What is the missing $$x$$ coordinate?

Which of these coordinates lie on the $$x$$ axis?

Which of these equations could be represented by this bar model?

Which of these equations are written in the form $$y = mx + c$$ ?

Finding the equation of the line ay + bx + c = 0

Lesson outcome