Question

myra uses an inverse variation function to model the data for the ordered pairs below.

(2, 30), (3, 20), (4, 15), (5, 12), (6, 10)

which statement best explains whether an inverse variation function is the best model for the data?

an inverse function is the best model because as \\(x\\) increases, \\(y\\) decreases.
an inverse function is the best model because the products of corresponding \\(x\\)- and \\(y\\)-values are equal.
an inverse variation function is not the best model because data points approximate a straight line.
an inverse variation function is not the best model because the data points show an exponential decay.

Explanation:

Calculate the product of each ordered pair

$$
LATEXBLOCK0
$$

Verify the definition of inverse variation

$$ x \cdot y = k \implies 60 = 60 $$

Identify the correct statement

$$ \text{The products of corresponding } x\text{- and } y\text{-values are equal.} $$

Answer:

• An inverse function is the best model because as x increases, y decreases.
• An inverse function is the best model because the products of corresponding x- and y-values are equal. (Correct answer)
• An inverse variation function is not the best model because data points approximate a straight line.
• An inverse variation function is not the best model because the data points show an exponential decay.