In direct variation, which statement is true about y and x?

In direct variation, which statement is true about y and x?

• A. The ratio y/x is not meaningful
• B. The ratio y/x is constant
• C. The ratio y/x equals x
• D. The ratio y/x equals y

Answer: (B)

Direct variation means y changes in proportion to x, so y = kx for some constant k. Because of this, when you form the ratio y/x (for x ≠ 0) you get y/x = k, a number that stays the same no matter what x is. That constant ratio is the signature of a direct variation. This rules out the idea that the ratio is not meaningful, since the ratio exists and stays constant (aside from the undefined case at x = 0). It also rules out the notions that the ratio equals x or equals y, which would require y to have specific forms (like y = x^2 or y = xy) that aren’t generally true for direct variation.

Direct variation means y changes in proportion to x, so y = kx for some constant k. Because of this, when you form the ratio y/x (for x ≠ 0) you get y/x = k, a number that stays the same no matter what x is. That constant ratio is the signature of a direct variation.

This rules out the idea that the ratio is not meaningful, since the ratio exists and stays constant (aside from the undefined case at x = 0). It also rules out the notions that the ratio equals x or equals y, which would require y to have specific forms (like y = x^2 or y = xy) that aren’t generally true for direct variation.