Recognize constant rate of change as evidence for a linear model.
Diagnose a nonlinear table
Problem
Analyze the displayed table. Test linearity using interval slopes, identify any stronger pattern and exact model the data support, and state the limits of the evidence.
One average slope cannot prove that a table is linear; every interval rate must agree. With equal input gaps confirmed, we’ll calculate all consecutive slopes, then inspect how those slopes themselves change. A stronger difference pattern can suggest another family and exact rule, though a finite table supports that rule only for the displayed data.
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