### Why do this problem?

This
problem encourages students to get into the real meaning of
equations and graphical representation without getting bogged down
in algebraic calculations or falling back into blind computation.
It will help to reinforce the differences between different 'types'
of equation.

### Possible approach

Note the difference between showing that an equation
is a possibility and
showing that it is not a
possibility. In the first case, students need only give a single
example of a curve with certain paramaters which passes through a
point of the required type. To show that an equation CANNOT pass
through a point of a certain type requires more careful
explanation. Hopefully students will work this out for themselves,
but prompt them if necessary.

### Key questions

- How can you tell if a certain point will match a certain
equation type?
- How can you tell if a certain point will not match a certain
equation type?

### Possible extension

### Possible support

Give concrete examples by labelling the points $(1, -1), (-1,
1), (-1, -1), (1, -1)$

Alternatively, try the easier non-algebraic question

Bio-graphs