If \(x\) and \(y\) are directly proportional, then which of the following is correct?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\displaystyle \frac{x}{y}=\) constant
Two quantities are directly proportional when they increase or decrease in the same ratio: doubling \(x\) doubles \(y\). That happens exactly when \(x=ky\) for a fixed \(k\), that is, \(\frac{x}{y}=k\).
Why the other options are incorrect
Option (1) \(x+y=\) constant — Incorrect. Here one quantity falls by the amount the other rises, so they do not change in the same ratio.
Option (2) \(x-y=\) constant — Incorrect. This keeps a fixed difference, not a fixed ratio: from (3, 1) to (6, 4) \(x\) doubles but \(y\) quadruples.
Option (3) \(xy=\) constant — Incorrect. This is inverse proportion: doubling \(x\) halves \(y\).