4 in a line further extended

the idea for this work comes from the very fine NRICH Diamond Collector task
in which students try to create straight lines that collect as many diamonds as possible:

there are three levels - increasingly complex


















the idea of the tasks below is that students try to find three straight lines
(none of which are vertical or horizontal)
passing through the 9 points

on each of the 3 lines, find a missing 4th coordinate pair to create 4-in-a-line

then find the equations of the 3 lines

(in the example there is more than one option; I hope that in the questions the three lines should each have 3 coordinates on them)