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