Question

Suppose y varies inversely with x, and y = -1 when x = 6. What inverse variation equation relates x and y?

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a. y = 6/x
b. y = -12x
c. y= -6x
d. y= -6/x​

Answer 1

d.
`\displaystyle y = (-6)/(x)`

Explanation:

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Answer 2

`\displaystyle \text{d. }y=(-6)/(x)`

Explanation:

If two values
`x` and
`y` are inversely proportional, their product is always some maintained constant (the product of
`x` and
`y` is always maintained). This way, if one goes up, the other must go down by the same extent. By definition, this represents an inversely proportional relationship.

Therefore, we can simply find this constant by multiplying the given values of
`x` and
`y`:

`xy=k,\\6\cdot (-1)=-6`

The constant
`-6` must be maintained as the product of
`x` and
`y` for all values of
`x` and
`y` for them to be inversely proportional. Thus, we have the equation:

`xy=-6`

Divide both sides by
`x` to isolate
`y`:

`\boxed{y=(-6)/(x)}`