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 are closer to forming a straight line.

An inverse variation function is not the best model because the data points show an exponential decay.

I got D is that correct??

try y = k/x

for (2,30)
30 = k/2
k = 60

for (5,12)
12 = k/5
k = 60 sure enough

x*y always = 60 (answer C)

nvm its a

NO !!!!!!

a straight line with
y = m x + b
with m negative so negative slope

would satisfy answer A
but the slope of these points is NOT constant

To determine whether an inverse variation function is the best model for the given data, we need to analyze the relationship between the x and y values. Inverse variation functions follow the form y = k/x, where k is a constant. Let's check the criteria for each statement:

A) "An inverse function is the best model because as x increases, y decreases."
This statement aligns with the behavior of an inverse variation function. As x increases, if y decreases or gets smaller, it indicates an inverse relationship.

B) "An inverse function is the best model because the products of corresponding x- and y-values are equal."
In an inverse variation function, the products of corresponding x- and y-values should remain constant. Let's calculate the products for each pair:
(2 * 30 = 60), (3 * 20 = 60), (4 * 15 = 60), (5 * 12 = 60), (6 * 10 = 60)
Since the products remain constant, this statement supports an inverse variation model.

C) "An inverse variation function is not the best model because data points are closer to forming a straight line."
An inverse variation function typically doesn't form a straight line. If the data points exhibit a linear pattern, it would suggest a different type of relationship.

D) "An inverse variation function is not the best model because the data points show an exponential decay."
An inverse variation function doesn't demonstrate exponential decay but rather an inverse relationship as stated previously. Exponential decay occurs when the data points decrease at a decreasing rate.

Considering the analysis above, statement A and statement B both support an inverse variation function as the best model for the data. Therefore, either A or B could be considered the correct answer.