In a direct proportion, as one quantity increases, the other:

In a direct proportion, as one quantity increases, the other:

• A. Increases by a fixed amount for every increase in the other quantity and the ratio stays constant.
• B. Increases by a fixed amount for every decrease in the other quantity and the ratio changes.
• C. Increases by a variable amount for every increase in the other quantity.
• D. Decreases by a fixed amount while the ratio stays constant.

Answer: (A)

Direct proportionality means the two quantities scale together with a constant ratio. If one quantity changes, the other changes by a fixed multiple of that change, so their ratio stays the same. In symbols, y = kx, so when x increases by Δx, y increases by Δy = kΔx. This keeps y/x equal to k for any values, so the other quantity grows in step with the first. That’s why the statement that the other quantity increases and the ratio remains constant is the correct description. The idea that the increase would be a fixed absolute amount unrelated to the size of the change, or that the increase could vary with x, or that one must decrease, does not fit direct proportionality.

Direct proportionality means the two quantities scale together with a constant ratio. If one quantity changes, the other changes by a fixed multiple of that change, so their ratio stays the same. In symbols, y = kx, so when x increases by Δx, y increases by Δy = kΔx. This keeps y/x equal to k for any values, so the other quantity grows in step with the first. That’s why the statement that the other quantity increases and the ratio remains constant is the correct description. The idea that the increase would be a fixed absolute amount unrelated to the size of the change, or that the increase could vary with x, or that one must decrease, does not fit direct proportionality.