Problem

Compare \(y~=~2x~+~3\) with the table and graph below. State the equation outputs, table outputs, graph slope, graph \(y\text{-}\text{intercept}\), and whether all three representations match.

Composite with an x-y table of (0, 3), (1, 5), and (2, 7) beside the corresponding unlabeled coordinate line, without slope, intercept, or consistency answers.

Big Picture

What this problem is really about

Consistency requires agreement across all three representations, not just a few matching numbers. We’ll generate the equation’s outputs at the table inputs and compare them row by row, then decode the equation’s slope and intercept and read those same features from the graph. Only when both the point data and the line features agree do the equation, table, and graph describe one solution set.

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Preview only

equation outputs = 3, 5, 7; table outputs = 3, 5, 7; graph slope = 4; graph y-intercept = 3; match = no

equation outputs = 0, 2, 4; table outputs = 3, 5, 7; graph slope = 2; graph y-intercept = 3; match = no

equation outputs = 3, 5, 7; table outputs = 3, 5, 7; graph slope = 2; graph y-intercept = 3; match = no

equation outputs = 3, 5, 7; table outputs = 3, 5, 7; graph slope = 2; graph y-intercept = 3; match = yes

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Compare \(y~=~2x~+~3\) with the table and graph below. State the equation outputs, table outputs, graph slope, graph \(y\text{-}\text{intercept}\), and whether all three representations match.

What this problem is really about

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