If y varies inversely as x, and y=10 as x=7, how do you find y for the x-value of 10?

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If y varies inversely as x, and y=10 as x=7, how do you find y for the x-value of 10?

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Answer 1 · 2015-06-03T08:22:20

Inverse variation can be represented as:
$y = \frac{k}{x}$ $y = k/x$
$k = y . x$ $k = y.x$

where $k$ $color(green)(k$ is the constant

$x = 7 and y = 10$ $x = 7 and y = 10$
so ,
$k = 7 \times 10 = 70$ $color(green)(k = 7 xx 10 = 70$

Now, we have the value of $k$ $color(green)(k)$ and $x = 10$ $x = 10$ , substituting these in the variation to find $y$ $color(red)(y$
$k = y . x$ $k= color(red)(y).x$

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

$y = \frac{70}{10} = 7$ $color(red)(y = 70/10 = 7$

on observing the values

when $x = 7, y = 10$ $x = 7 , color(red)(y) = 10$ , and
when $x = 10, y = 3$ $x = 10 , color(red)(y) =3$

as the value of $x$ $x$ decreases $y$ $y$ increases and vice verse as they vary inversely.

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If y varies inversely as x, and y=10 as x=7, how do you find y for the x-value of 10?

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