Identify linear functions from tables

Use first differences in tables to determine whether a relation is linear.

Lesson 5

Concept

In a table, a linear function shows equal changes in y for equal changes in x.

Table A increases by +4 each row; Table B increases by +2, +5, +3. Determine which is linear.

If y changes by +3 whenever x changes by +1, the table is:

Linear

Not linear

Quadratic

Cannot tell

Which y-values suggest nonlinearity for x = 1,2,3,4?

5, 8, 11, 14

2, 6, 12, 20

-1, 1, 3, 5

0, 4, 8, 12

These steps are out of order — can you fix them?

1.Compute first differences

2.Justify with data

3.Classify as linear/nonlinear

4.Compare differences

Why are first differences useful?