Find an equation of variation in which y varies inversely as x and the following is true:
y=31, when x=4
Originally, I mixed up the equations of inverse and direct variation, and got 31=m(4)
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b
Obviously, I got it wrong, but I've gone ahead and redid the problem, and I'd just like somebody to check it for me:
y=k/x
31=4K
(divide both sides by 4)
y=7.75
x y = k
To find the equation of variation in which y varies inversely as x, we start with the general equation:
y = k/x
where k is the constant of variation.
To find the value of k, we can substitute the given values of y and x into the equation. We are given that when x=4, y=31. Plugging these values into the equation, we get:
31 = k/4
To solve for k, we can multiply both sides of the equation by 4:
31 * 4 = k
k = 124
Now that we have the value of k, we can substitute it back into the equation to get the final equation of variation:
y = 124/x
Therefore, the correct equation of variation in which y varies inversely as x is y = 124/x.