Using dynamic software to explore linear relationships

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.

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?

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