Using dynamic software to explore linear relationships

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

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

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

For relationships in the form $$y=mx+c$$ the value of $$m$$ determines the {{ }}.

One and only one of the lines will have a negative gradient.

They will all have a different $$y$$-intercept.

What of these statements will be true about the lines $$y=3x$$, $$y=7x$$, and $$y=-2x$$?

Which statements are true about the lines $$y=x+5$$, $$y=x+9$$, and $$y=x+0.5$$?

The lines $$y=4-7x$$ and $$y=-0.1-7x$$ have the same {{ }}.

Relationships in the form of $$y=mx+c$$ will give us a {{ }}.

Which of these coordinates sits on the $$y$$-axis?

This table of values will plot a linear relationship with what gradient?

Using dynamic software to explore linear relationships

Lesson outcome