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Question 2 of 5
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After buying a car, Sarah decides to get it appraised every few years. After owning the car for two years, its value is $5,000. After own
the car for five years, its value is $2,000.
What is the equation that models this inverse variation?
Oy=
O y = 2,500
O
O
5,000
y = 2,000
y =
10,000
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Respuesta :

The inverse proportional relationship that models this variation is given as follows:

[tex]y = \frac{10,000}{x}[/tex]

What is a proportional relationship?

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

An inverse proportional relationship is given as follows:

[tex]y = \frac{k}{x}[/tex]

In this problem, we have an inverse relation in which y(2) = 5000, hence the constant k is found as follows:

[tex]y = \frac{k}{x}[/tex]

[tex]5000 = \frac{k}{2}[/tex]

k = 10,000

Hence the relation is:

[tex]y = \frac{10,000}{x}[/tex]

As stated in the problem, when x = 5, y = 2,000, which we can verify replacing in the relation.

More can be learned about proportional relationships at https://brainly.com/question/10424180

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