In an inverse variation, the product x y is constant. If (x1, y1) and (x2, y2) are solutions of

step 1 So here is a question of inverse variation. So in inverse variation we know that Product of two

In an inverse variation, the product x y is constant. If...

In an inverse variation, the product $x y$ is constant. If $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right)$ are solutions of $x y=k,$ then $x_{1} y_{1}=x_{2} y_{2} .$ Use this equation to find the missing value.
Find $x_{2}$ when $x_{1}=9, y_{1}=-3,$ and $y_{2}=12$.

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Key Concepts

Inverse Variation

Inverse variation refers to a relationship between two variables where their product is constant. In other words, if one variable increases, the other decreases such that the product of the two remains unchanged. This relationship is commonly represented by the equation xy = k, where k is a constant.

Constant Product

The constant product is the fixed value obtained when multiplying the two variables in an inverse variation relationship. This value remains the same across all pairs of corresponding variables and is essential for solving problems where one variable is missing.

Solving for Missing Values Using the Constant Product

In an inverse variation problem, to find a missing value, you determine the constant product using known values. Once the constant is established, you can solve for the unknown variable by dividing the constant by the known variable. This method is a straightforward application of the invariant nature of the product in inverse variations.

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