Determine whether a relationship is proportional from a table, graph, equation, or context.
Check proportionality from a graph
Problem
A graph of distance versus time shows points at \((0,~0)\), \((2,~6)\), \((4,~12)\), and \((6,~18)\) connected in a straight line. Is this relationship proportional?
A proportional graph must satisfy two conditions together: one straight-line rate and passage through the origin. We’ll inspect whether all plotted points lie on a single line, verify that zero time aligns with zero distance, and compare distance divided by time at the nonzero points. Those checks determine the classification without comparing unlike axis increments.
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