Find and interpret the constant of proportionality in multiple representations.
Choose a smart first step for finding k
Problem
A proportional graph includes \((4,10)\). Consider these methods for finding \(k\): A, add \(x+y\); B, divide \(y/x\); C, subtract \(x\) from \(y\); D, find the midpoint. Choose the method that works, then calculate \(k\) in \(y\text{-}\text{units}~\text{per}~x\text{-}\text{unit}\).
The constant on a proportional graph describes y-units for each one x-unit, so a valid method must calculate output divided by input. We’ll evaluate the proposed operations against that meaning, substitute the coordinates from the labeled point in y-over-x order, and simplify the quotient. Adding, subtracting, or finding a midpoint answers a different question.
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