Determine whether a relationship is proportional from a table, graph, equation, or context.
Name the feature that determines proportionality
Problem
A straight graph crosses the \(y\text{-}\text{axis}\) at \(3\). Classify the relationship and state its determining feature: passes through \(\text{origin}\), nonzero \(y\text{-}\text{intercept}\), constant \(y/x\), or form \(y=kx\).
Big Picture
What this problem is really about
Straightness gives a constant slope, but a proportional graph must also pass through the origin. We’ll identify the point where the line crosses the y-axis, compare that point with zero comma zero, and name the feature that controls the classification. This separates a general linear relationship from the stricter proportional case.
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