Question

If y varies inversely with x, and x = -10 when y = 60. How do you find the inverse variation equation and use it to find the value of y when x = 15?

Answer 1

The equation is `y=-600/x`

At `x=15` the value of `y` is - 40

Explanation:

Set `y=1/x xx k ->k/x`

Given condition `(x,y)->(-10,60)`

So by substitution we have:

`color(green)(y=k/x" "->" " 60=k/(-10))`

Multiply both sides by `color(red)((- 10))`

`color(green)(60color(red)(xx(-10))=k xx(color(red)(-10))/(-10))`

But `(-10)/(-10)=+1`

`-600=k`

Giving: `y=k/x" "->" "y = -600/x`
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Suppose `x=15` as in the question. Then we have:

`y=-600/15 = -40`

Answer 2

`y = -40`

Explanation:

In an inverse variation, as one quantity increases, the other one decreases.

`y` varies inversely with `x` can be written as: `" "y prop 1/x`

A proportion can be made into an equation by using a constant:

`y prop 1/x " "rarr" "y = color(red)(k)/x" "rarr" " color(red)(k)= x xx y`

Use the two values given to find the value of `k:`

`color(red)(k) = -10 xx60 =color(red)( -600)`

The equation can therefore be written as: `" "y = color(red)(-600)/x`

Now we know the exact relationship between `x` and `y`

If `x = 15" " y = -600/15 = -40`