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
since xy = k, and
0.2*2 = 0.4,
xy = 0.4
or,
y = 0.4/x
Still correct 8 years later, and he just helped me figure out how inverse variation worked.
You are a great help.
7 yrs later and still correct :)
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!
How about this equation: y = 0.4 divided by x.
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!
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