# 2.2 Variables

If we had a pattern that went 0, 2, 4, 6, 8, 10. Instead of using one line, we can introduce 2 lines, such that we now have:

 x 0 1 2 3 4 5 y 0 2 4 6 8 10

Instead of saying that the y-values (i.e. second row) is increasing by 2, we can say the y is twice what x is.

This is a lot more beneficial, because we know that if we assign $x=20$, y is double, or $y=20*2=40$

In the scenario that we didn’t know that y is twice x (i.e. $y=2*x$, or alternatively, $y=2x$), we would have had to extend the table much further to the right to find the correct answer, which is inefficient!

Another example:

 x 0 1 2 3 4 5 y 1 3 5 7 9 11

Note this time, that even though the increment is by 2, it is NOT $y=2x$ any more. Rather, it is $y=2x+1$. As above, if we know $x=40$, $y=40(2)+1=81$.

The above questions are therefore an example of “finding the formula”. Alternatively, there may be an instance where you have to insert in an x, to obtain a y.