Identifying a possible non-linear rule for a given table of values

# Identifying a possible non-linear rule for a given table of values

#### Question 1

The relationship between two variables, x and y, is shown in the table.

x | 0 | −1 | −2 | −3 |
---|---|---|---|---|

y | 1 | 3 | 9 | 19 |

Which equation best describes the relationship between x and y ?

y = 1− 2x² | y = 2x + 1 | y = 2x² + 1 | y = 1− 2x |

#### Solution

First note that when the points are plotted they do not lie on a straight line. We say the relationship is non-linear.

#### Example of a linear graph

Note: For linear graphs the change in the y value as the x value increases by one is always the same. In the example to the right: as the x value increases by 1, the y value decreases by 2.

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