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 are closer to forming a straight line.

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

Answer 1

"Note how for each (x,y) pair of points given we see that x*y = 60 
For instance, the point (4,15) has x = 4 and y = 15 so x*y = 4*15 = 60 
Another example: (x,y) = (6,10) means x = 6 and y = 10, so x*y = 6*10 = 60 
The fact that this is true for ALL of the points shown indicates we have an inverse variation of the form x*y = k where k = 60 in this case. 
Therefore, the answer is B.) An inverse function is the best model because the products of corresponding x- and y-values are equal."

Answer 2

The statement that best explains the inverse variation model is (b) an inverse function is the best model because the products of corresponding x- and y-values are equal.

How to determine the true statement?

An inverse model is represented as:

k = xy

This means that the product of the x and y values must be constant.

From the dataset, we have:

2 * 30 = 3* 20 = 4* 15 = 5 * 12 = 6 * 10 = 60

This means that the products of corresponding x- and y-values are equal.

Hence, the true statement is (b)

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