Home/Integrated Math 1/Lesson 52

Identify linear functions from tables

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

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Lesson 52 of 192

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Concept

Objective: Students will classify tables as linear or non-linear using first differences.

Estimated Time: 12 minutes

Standards:

HSF-IF.B.4HSF-LE.A.1

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

Try it

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

Concept Check

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

Linear

Not linear

Quadratic

Cannot tell

Concept Check

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

Common Misconception

Always verify your result in context instead of trusting a first pass.

Table analysis flow

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

1.Justify with data

2.Classify as linear/nonlinear

3.Compare differences

4.Compute first differences

Short Answer

Why are first differences useful?

Mastery Check

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Question 1