Recognize constant rate of change as evidence for a linear model.
Find the input value when a linear model reaches a given output
Problem
For the linear model \(f(x)=4x+7\), find the \(x\)-value when the output reaches \(31\).
Big Picture
What this problem is really about
The target number here is an output, so the task runs the linear model backward to recover its input. We’ll set the function expression equal to that target, undo the added constant, and then undo the multiplication by the rate. Substitution into the original model will verify that the recovered input produces the required output.
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