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Suppose that x and y vary inversely and that x=10 when y=8. write the function that models the inverse variation. find y when x=5

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As the variables vary inversely, we have the following relationship:

y = k / x
From here, we must find the value of the constant k.
For this, we use the following data:
x = 10 when y = 8
Substituting values we have:

8 = k / 10
From here, we clear the value of k:

k = (8) * (10) k = 80
Substituting the value of k we have that the function is:

y = 80 / x
Then, for x = 5 we have:

y = 80/5 y = 16
Answer:
The function that models the inverse variation is:

y = 80 / x
when x = 5:

y = 16
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