So I missed the #beingmathematical chat this week but was inspired by some of the outcomes.

The original task was this:

I spotted @dannytybrowns responses including this one (and the thread that follows) and thought I'd have a little play on geogebra too.

I made a simple interactive to start. I included the introduction part as I felt it helps to understand what is happening:

I really enjoyed having a play. I noticed patterns for whole numbers, both positive and negative. I also enjoyed playing with fractional a values, and negative fractional a values. I liked the patterns that came from this sequence: -1/6, -2/5, -3/4, -4/3, -5/2, and -6.

I then added a new variable to play with.

I particularly liked this pattern:

I also made this one here where equally spaced points along the line are shown.