Assume y varies inversely as x, how do you write the equation given y=-4 when x=16?

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Assume y varies inversely as x, how do you write the equation given y=-4 when x=16?

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Answer 1 · 2017-03-24T13:27:44

$y = - \frac{64}{x}$ $y=-64/x$

Explanation:

The statement is expressed as $y \propto \frac{1}{x}$ $yprop1/x$

$inverse means \frac{1}{variable}$ $"inverse means " 1/("variable")$

To convert into an equation introduce k, the constant of variation.

$\Rightarrow y = k \times \frac{1}{x} = \frac{k}{x}$ $rArry=kxx1/x=k/x$

To find k use the condition that y = - 4 when x = 16

$\Rightarrow y = \frac{k}{x} \Rightarrow k = y x$ $rArry=k/xrArrk=yx$

$\Rightarrow k = - 4 \times 16 = - 64$ $rArrk=-4xx16=-64$

$"Equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=-64/x)color(white)(2/2)|)))$

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Assume y varies inversely as x, how do you write the equation given y=-4 when x=16?

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