Question

Look at the data tables below.



Which would most likely produce a nonlinear graph?

Table 1
Table 2
Table 3
Table 4

Answer 1

I don’t see the four data tables in your message. If you paste them I can pick which one is nonlinear.

Meanwhile, here’s a quick way you can tell which table will make a nonlinear graph:

- If the x-values increase by a constant amount, compute the differences in the y-values (y2−y1, y3−y2, …).
- If those first differences are all the same, the graph is linear.
- If the first differences are not constant but the second differences (differences of the differences) are constant, the graph is quadratic (nonlinear).
- If the y-values change by a constant factor (ratios y2/y1, y3/y2, … are all equal), the relationship is exponential (nonlinear).
- If neither differences nor ratios show a simple pattern, the graph is nonlinear in a less simple way.

Examples:
- x: 1,2,3 y: 2,4,6 → first differences 2,2 → linear.
- x: 1,2,3 y: 2,4,8 → ratios 2,2 → exponential (nonlinear).
- x: 1,2,3 y: 1,4,9 → first differences 3,5 (not constant), second differences 2 → quadratic (nonlinear).

Paste the four tables and I’ll identify which one is most likely nonlinear.