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

To understand the relationship described, we need to know what it means for one variable to be inversely proportional to another. When a variable x is inversely proportional to another variable y, it means the product of x and y will always be a constant. Mathematically, this relationship can be expressed as:

x * y = k

Here, k is the constant of proportionality.

According to the problem, when x = 9, y = 4. Substituting these values into the equation gives:

9 * 4 = k

Calculating this, we get:

k = 36

Therefore, the equation representing the relationship between x and y is:

x * y = 36

Rearranging this to show x in terms of y, we have:

x = 36/y

Given the options, x = 36y is the correct choice that satisfies the inverse proportionality between x and y, where the constant product is 36.