Question

The variables x and y vary inversely. Use the given values to write an equation that relates x and y. $$x=11, y=2$$

Short answer

The equation that relates x and y is \(xy = 22\).

Step-by-step solution

Understand inversely proportional relationship

First you know from the problem that x and y have an inversely proportional relationship. This means that if x increases, y decreases and vice versa. In mathematical terms, we can denote this relationship as \(xy = k\), where k is a constant.

Substitute the known values

Take the known values x and y (which are 11 and 2, respectively) and substitute them into the equation. Therefore, it becomes \(11 * 2 = k\), which simplifies to \(k = 22\).

Formulate the final equation

Now, we can express the relationship between x and y using our found constant k. The final equation thus becomes \(xy = 22\). This equation describes the inversely proportional relationship between x and y, and you will obtain the same result for k regardless of the x and y values you choose, as long as they adhere to the original constraint of x and y being inversely proportional.