If x is inversely proportional to y and x = 9 when y = 4, find the law containing x and y

Analyze the question: We are told x is inversely proportional to y, and we need the equation (law) linking x and y using the given values.

Concept: If x is inversely proportional to y, then

x ∝ 1/y, so x = k/y, where k is a constant.

Solution:

1. Write the relationship: x = k/y
2. Substitute x = 9 and y = 4: 9 = k/4
3. Solve for k: k = 9 × 4 = 36
4. Put k back into the law:

x = 36/y

Check: When y = 4, x = 36/4 = 9 ✓

Why the others are wrong:

• A: 16/4 = 4, not 9.
• C: y/36 is a direct relationship, not inverse.
• D: 13/4 = 3.25, not 9.

Answer: B

Tip: For inverse proportion, the product xy is always constant (k). Just multiply the given values (9 × 4 = 36) and write x = k/y. For direct proportion, divide instead (k = x/y).