### Why do this problem?

This resource allows students to explore the connection between
a straight line on a graph and the equation that represents or
defines it - equations of the form $y = mx + c$. Students are
encouraged to conjecture and test their conjectures.

### Possible approach

It is useful if students have also done some preliminary work
plotting straight line graphs.

Working with the whole group demonstrate the interactivity,
moving both points to allow the group to see the freedom the line
has. Draw attention to the equation of the line showing beneath the
graph.

Take time to discuss how an equation represents a line by
defining the set of points that lie along it. Select points on the
line to demonstrate how the coordinates of the point satisfy the
equation. Ask questions to challenge this understanding, like: find
the equation of a line that goes through (2,3); find the equation
of a steeper line; find the equation of a line that slopes down
instead of up.

The second interactivity allows the equations of two
independent lines to be compared. Working in pairs at computers ask
students to propose equations of parallel lines and use the
interactivity to check their suggestions.

Encourage students to refine their earlier conjectures. Ask
them to phrase what they have learned about equations of straight
lines in exactly 25 words.

When students feel they understand this completely, suggest
they play

Diamond Collector in pairs or against the computer. Allow them
to close the game and go back to the parallel lines interactivity
if they find they need to learn a bit more to help them play the
game better.

### Key questions

What are the connections between the properties of a line and
its equation?

What does parallel mean?

How do the equations of parallel lines relate to each other
and why is that?

If I give you a rule, can you predict what the graph will look
like without having to plot it?

### Possible extension

Students can extend their understanding by considering the
relationship between lines which are perpendicular, establishing
the validity of the standard result rather than merely remembering
it. This is the task in the related problem

Perpendicular Lines

Which is
Bigger? offers students the chance to apply their understanding
of straight line graphs.

### Possible support

Concentrate on the first interactivity until the relationship
between a line's properties and its equation are well understood.
Ask students to predict what the graphs of different equations will
look like and then use the interactivity to test their
predictions.