Suppose that y varies inversely with x and that y = 2 when x = 8. What is an equation for the inverse variation?

Answer 1

If y varies inversely with x, it means that y and x have a constant product. Let's call this constant k. Then, we can write:

y * x = k

If we know that y = 2 when x = 8, we can substitute these values into the equation and solve for k:

2 * 8 = k
k = 16

Now we can write the equation for the inverse variation as:

y * x = 16

Or, if we want to solve for y:

y = 16 / x