The coordinates prompt was designed by Caitriona Martin (see box). It has the potential to develop an understanding of:
- Plotting coordinates in four quadrants;
- The gradient of a line (and parallel and perpendicular lines);
- The y-intercept;
- Coordinate shapes when the coordinates are viewed as vertices;
- Other coordinates on the line that joins the two coordinates.
The gradient of the line that joins the two coordinates is -1/2, which could be challenging for some classes. A more appropriate prompt to introduce graphs of linear equations might use two coordinates that have a clearer connection between the x- and y-coordinates. For example, in (2,5) and (4,7) the y-coordinate is three greater than the x-coordinate. Thus the equation of the line is y = x + 3 and other coordinates on the line are of the form (n,n + 3). Similarly, the coordinates (-1,3) and (3,11) are on the line y = 2x + 5 and have the general form (n,2n + 5). Another option for the prompt is to give three coordinates from which students would be able to infer a generalisation more securely.