Two Number Lines

We had particularly good solutions from Callum at St Patrick's School, Boyang from Mountfields Lodge and Caroline from St Jude's C of E School. Caroline wrote:

Max's secret jump was 3, 10-7=3
Mandy's secret jump was 3, 6-3=3
On the grid, Max had moved 9 along and Mandy had moved 3 up.

She goes on to say:

If Max and Mandy both move the same distance along and up, the counter could be at:
0 along and 0 up
1 along and 1 up
2 along and 2 up
3 along and 3 up
4 along and 4 up
5 along and 5 up
6 along and 6 up
7 along and 7 up
8 along and 8 up
9 along and 9 up
10 along and 10 up
This line is a diagonal line.

That's right! Boyang and Callum gave the coordinates of the points. Callum said:

(0,0) or (1,1) or (2,2) or (3,3) or (4,4) or (5,5) or (6,6) or (7,7) or (8,8) or (9,9) and could go on forever.