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?

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Answer 1 · 2017-02-17T17:29:50

The equation is $y=-600/x$

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

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 · 2017-02-17T18:41:11

$y = -40$

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 $x = 15" " y = -600/15 = -40$