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If we assume a constant inverse relationship then we can start with the equation y = c/x where c is the constant of proportionality. Plugging in the known values of x = 7 and y = 5 we determine that c = 35. We now have the equation of y = 35/x. Plugging in 4 for x we see that y = 35/4 = 8.75.

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Q: If y varies inversely with x and y equals 5 when x equals 7what is the value of y when x equals 4?
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If y varies inversely as x and y equals 3 when x equals 6 find the value of x when y equals 18?

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So 5 = (xy)^2 and x = 2.5. This means that 5 = (2.5y)^2. So sqrt(5)/2.5 = y when x = 2.5. Now if x = 9 then 5 = (9y)^2. So sqrt(5)/9 = y. This means that for any x in this relation y = sqrt(5)/x.


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