Two quantities $x$ and $y$ are in direct proportion. Which relation always holds?

Two quantities $x$ and $y$ are in direct proportion. Which relation always holds?
  1. $x \cdot y = k$ (constant)
  2. $\dfrac{x}{y} = k$ (constant)
  3. $x + y = k$
  4. $x - y = k$

Solution

By definition of direct proportion, $\dfrac{x}{y}$ stays constant; equivalently $x = k y$.

Asked in: IMO

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