Find and interpret the constant of proportionality in multiple representations.
Find k from a graph
Problem
A proportional relationship is graphed as a straight line through the origin. Points on the graph include \((2,~5)\) and \((4,~10)\). What is the constant of proportionality, \(k\)?
For a proportional line through the origin, k is the vertical output per horizontal input. We’ll use a nonzero plotted point, divide its y-coordinate by its x-coordinate, and then repeat with the other labeled point. Matching quotients confirm the line’s constant multiplier and prevent reversing the ratio.
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