Is the relationship shown by the data linear? If so, model the data with an equation. The relationship is not linear.

Answer 1

- To check if the relationship is linear, see if the ratio of the change between y-values and the change between x-values is consistent. After putting them in increasing order of the x-values. Here's an example:

x | 2 | 4 | 8

y | 1 | 4 | 10

In horizontal table of values above, the x-values are in increasing order (least to greatest), so we can analyze.

> The first change

- The change from the x = 2 to x = 4 is +2.

- Matching those x-values, the change from y = 1 to y = 4 is +3.

- So we have a ratio of change of +2/+3, or simply 2/3

> The second change

- The change from the x = 4 to x = 8 is +4

- Matching those x-values, the change from y = 4 to y = 10 is +6.

- So we have a ratio of change of +4/+6, which you can simplify as 2/3 (dividing by 2).

> Since the ratio of change 2/3 is consistent, we have a linear relationship!

- Remark that my data set only had 3 points, if there are more, you must check that the rate of change is consistent each time. If it is different just even once, it's not linear.

> Now if it is linear, to find an equation:

- Use to points of the set and do slope formula to find the slope.

- Use the slope you find with one of the points to either plug in y = mx + b and find b, or into point-slope form.

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