Suppose that x and y vary inversely when x = 1 and y = 7. Write a function that models the inverse variation. Graph the function and find y when x = 20.

Question

Write a function that models the inverse variation.

y

Answer 1

= k/x

where k is a constant of variation.

To find k, we use the initial values x = 1 and y = 7:

7 = k/1
k = 7

So the function that models the inverse variation is:

y = 7/x

Now, let's graph the function:

y = 7/x

To find y when x = 20, we substitute x = 20 into the function:

y = 7/20
y = 0.35

Therefore, when x = 20, y = 0.35.