Question

Suppose that x and y vary inversely, and x = 12 when y = 8 . Write the function that models the inverse variation.

Answer 1

96/x

Explanation:

When two variables x and y vary inversely, their product is a constant. Therefore, the function that models the inverse variation between x and y is:

x*y = k

where k is the constant of proportionality.

We can use the given information to find the value of k:

x = 12 when y = 8

so, k = xy = 128 = 96

Now we can use this value of k to write the function that models the inverse variation:

x*y = 96

To find the inverse variation, we divide both sides by y,

x = 96/y

Alternatively, we can write y = 96/x

So, the function that models the inverse variation between x and y is either x = 96/y or y = 96/x