Depth · one concept from first principles · step 2 of 4
Liam only misread a, so his y-intercept is right. His line crosses the y-axis at (0, 2).
Ignore Liam's slope; keep his intercept.
8.F.A.3Change Focus Count The ComplementLiam's line still shows the true , and Mia's line still shows the true .
At the term is , and adding to leaves , so the -intercept depends only on , which Liam read correctly.
Changing adds the same amount to every output, which leaves every rise between two points unchanged, so the slope depends only on , which Mia read correctly.
Mia only misread b, so her slope is right. Her line passes through (0, -2) and (2, 0).
Ignore Mia's intercept; keep her slope.
8.F.B.4Draw A DiagramUse the correct slope and the correct intercept.
Each wrong graph contributed exactly one true coefficient.
8.F.A.3Convert To AlgebraA wrong graph isn't useless -- ask which part the student got right, and keep exactly that part.
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The same shape shows up later on the AMC, as Arithmetic Expression Decomposition, Branching State Enumeration, Multiplicative Ratio with Integrality Constraints. Why the shapes repeat →