Suppose y varies inversely with x, how do you write an equation for the inverse variation if y = 8 when x = 1/2?

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Suppose y varies inversely with x, how do you write an equation for the inverse variation if y = 8 when x = 1/2?

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Answer 1 · 2015-06-02T15:04:00

Since it is an inverse variation it can be represented as:
$y = \frac{k}{x}$ $color(red)(y) = color(blue)(k/color(red)(x$ , where $k$ $color(blue)(k$ represents the constant term , $x and y$ $color(red)(x and y)$ are the variables.

Values for the variables are:
$y = 8$ $y=8$ and $x = \frac{1}{2}$ $x=1/2$

substituting these values :
$y = \frac{k}{x}$ $color(red)(y) = color(blue)(k/color(red)(x$
$y . x = k$ $color(red)(y.x) = color(blue)(k$

$\frac{1}{2} . 8 = k$ $1/2 . 8 = color(blue)(k)$
we get the constant as $k = 4$ $color(blue)k = 4$

$y = \frac{4}{x}$ $color(red)(y) = color(blue)(4/color(red)(x$

$x . y = 4$ $color(red)(x.y) = color(blue)(4$ , represents the inverse variation in which constant is $4$ $4$ .

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Suppose y varies inversely with x, how do you write an equation for the inverse variation if y = 8 when x = 1/2?

1 Answer

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