4 in a line extended

this work extends the introduction to coordinates and the equations of simple straight lines
(i.e lines that are: vertical, horizontal, parallel to y = x and parallel to y = -x)
into negative quadrants

this work can usefully introduce or reinforce the procedure for subtracting a negative (the 'geometrical/algebraic imperative' as Hans Freudenthal calls it)

students find a 4th coordinate to complete 4-in-a-line
and then try to find a rule for the lines

these rules only involve gradients of plus 1 and minus 1

the powerpoint is here