Ed from St Peters College noticed that:

If the numbers aren't changed ($\times2$ and $+3$), the final answer will always be odd.
When the values of the $2$ and $3$ are changed, from an even and an odd, to an odd and an even, the answer will be the same type as the number placed in the input box at the start:
if the input is even, the answer will be even
if the input is odd, the answer will be odd

Thomas from Wilson's School noticed that:

The higher the numbers you are multiplying by, the steeper the gradient of the graph.

The addition or subtraction determines where the graph cuts the y-axis.

Rajeev from Fair Field Junior School in Radlett summarised his findings clearly here
He started to consider the equations of perpendicular lines. You can go to Perpendicular Lines if you would like to explore this further.