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.

Alternative solution: by substitution