Identify the constant k in y = kx from a table, graph, equation, or verbal description, and recognize whether a table or relationship is proportional (constant y/x).
Free, timed SHSAT practice sets on constant of proportionality— every question includes a full worked explanation, and there's no account required.
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In a proportional relationship \(y = kx\), the constant of proportionality \(k\) is the amount of \(y\) for one unit of \(x\):
\(k = \dfrac{y}{x}\)
Common traps: dividing \(x\) by \(y\) (that gives \(\frac{1}{k}\)), reading \(k = 20\) from \(5y = 20x\) without dividing by 5, and reporting \(y\) itself instead of \(y \div x\).
\(k = y \div x = 9 \div 3 = 3\). (Dividing \(x\) by \(y\) gives about 0.333. Stopping at \(y\) without dividing gives 9. Multiplying \(3 \times 9\) instead of dividing gives 27.)
Divide both sides by 6: \(y = \dfrac{15}{6}x\), so \(k = 2.5\). (Dividing 6 by 15 instead gives 0.4. Using the coefficient of \(x\) without dividing by 6 gives 15. Using the coefficient of \(y\) gives 6.)
Check whether \(y/x\) is the same at both listed points. \((2,6),(4,12)\) give \(6/2 = 12/4 = 3\); \((3,9),(5,15)\) give \(9/3 = 15/5 = 3\); \((1,4),(3,12)\) give \(4/1 = 12/3 = 4\) -- all constant, so all three are proportional. The other two change ratio between their points, so they are not proportional.