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If y varies inversely as x, and x=-1 when y=3, what is x when y is 15?

User Specur
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1 Answer

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Explanation:

If y varies inversely as x, it means that their product is constant. We can write this relationship as y x k = constant, where k is the constant of variation.

To find the value of k, we can use the initial values given: "x=-1 when y=3". Substituting these values into the equation gives us:

3 x k = constant

We don't need to know the value of the constant, just that it is the same throughout. Now we can use this relationship to find x when y is 15:

y x k = constant

15 x k = constant

We can solve for x by isolating it:

15 x k = constant

x = constant / k

Since the constant is the same throughout, we can use the initial values to find k:

3 x k = constant

-1 x k = constant

Dividing these equations gives us:

3 / (-1) = -k / k

-3 = -k^2 / k

Simplifying:

k = -k^2 / 3

Multiplying both sides by -3:

3k = k^2

Rearranging:

k^2 - 3k = 0

Factorizing:

k(k - 3) = 0

So k = 0 or k = 3.

Since k cannot be zero (otherwise y would be zero for all x), we can use k = 3. Therefore, the equation is:

y x 3 = constant

Using this equation to find x when y is 15:

15 x 3 = constant

x = constant / 45

We don't need to know the value of the constant, just that it is the same throughout. Therefore, when y is 15, x is equal to constant divided by 45.

Hopes this helps

User Alex Rockwell
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