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.