Question 1088778: 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?
A.) An inverse function is the best model because as x increases, y decreases.
B.) An inverse function is the best model because the products of corresponding x- and y-values are equal.
C.) An inverse variation function is not the best model because data points are closer to forming a straight line.
D.) An inverse variation function is not the best model because the data points show an exponential decay.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
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.
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Side Notes:
Note1: The term "product" means "result of multiplication". For example, the product of 2 and 5 is 10. In other words, 10 is the product after the result of multiplying 2 and 5.
Note2: Choice A is correct to a certain degree. For any inverse variation, as x increases, y will decrease (and vice versa). We have a sort of "opposites" dynamic going on here. However, this isn't strong enough of a condition. There are other functions that have this property. One such example are linear functions with negative slope. Inverse variation functions are not linear.
Note3: Solve x*y = 60 for y to get y = 60/x, which is the same as f(x) = 60/x. This will graph out a hyperbola with asymptotes as the x and y axis.
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