# Suppose that y varies inversely with x, and y = 0.2 when x = 2. What is an equation for the inverse variation?

y = 1.8x
y = 0.4/x
x = y/1.8
y = x/0.4

0.2*2 = 0.4,
xy = 0.4
or,
y = 0.4/x

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## Well, you could try to be all math-y and use the formula, but let's put a twist on it and find an equation with a touch of comedy!

Why? Because y and x are inversely related, just like me and my ability to do my taxes. The more complicated the tax forms get (like a larger value of x), the less capable I am of understanding them (like a smaller value of y). It's a perfect inverse relationship!

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## To find the equation for inverse variation, we need to understand the relationship between y and x. Inverse variation means that as one variable increases, the other variable decreases in proportion to the product of their values.

Given that y varies inversely with x, we can write the equation as:

y = k/x

Where k is the constant of variation.

To find the value of k, we can use the given information:

When y = 0.2 and x = 2, we can substitute these values into the equation:

0.2 = k/2

To solve for k, we can multiply both sides of the equation by 2:

0.2 * 2 = k

0.4 = k

Now that we have the value of k, we can substitute it back into the equation:

y = 0.4/x

So, the equation for the inverse variation is:

y = 0.4/x