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 , *y* is double, or

In the scenario that we didn’t know that *y* is twice *x* (i.e. , or alternatively, ), 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 any more. Rather, it is . As above, if we know , .

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*.

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