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M1-029-A10-V03
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F-LE.1.b
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M1-029-A10-V03
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, determine whether the data establish a stronger nonlinear pattern or exact model, and state the limits of the evidence.
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A
slopes = 5 and 3 using output differences only; verdict = not linear because these differ; stronger pattern = points are not collinear; conclusion = no unique nonlinear family; scope = input interval widths do not matter
B
slopes = 5/2 and 1 over unequal intervals; verdict = not linear because slopes differ; stronger pattern = points are not collinear; conclusion = no unique nonlinear family is established; scope = three uneven points need an assumed family or more data
C
slopes = 5/2 and 1 over unequal intervals; verdict = not linear because slopes differ; stronger pattern = any three noncollinear points fit a quadratic; conclusion = quadratic is proven; scope = no more data are needed
D
slopes = 5/2 and 1 over unequal intervals; verdict = linear because outputs increase; stronger pattern = no further test; conclusion = y increases linearly; scope = any increasing points prove linearity
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Curriculum context
Standard F-LE.1.b
Category Functions
Domain Linear, Quadratic, and Exponential Models
Objective Recognize constant rate of change as evidence for a linear model.
Problem type Diagnose a nonlinear table
