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:

Step1: Recall inverse variation rule

For inverse variation, $x \times y = k$ (constant $k$).

Step2: Calculate $x \times y$ for each pair

$2 \times 30 = 60$, $3 \times 20 = 60$, $4 \times 15 = 60$, $5 \times 12 = 60$, $6 \times 10 = 60$

Step3: Evaluate each option

First option is insufficient (decrease alone doesn't confirm inverse variation). Third/fourth are false (data doesn't fit line/exponential decay). Second matches our calculation.

Answer:

An inverse function is the best model because the products of corresponding x- and y-values are equal.