If y varies inversely as x, and y = 12 as x = 2, how do you find y for the x-value of 6?

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Answer 1 · 2016-07-09T15:56:06

$x = 4$ $x=4$

As $x$ $x$ and $y$ $y$ are inversely proportional, the equation can be represented as $x = \frac{k}{y}$ $x = k/y$ .

Substituting $x = 2$ $x=2$ and $y = 12$ $y=12$ , we get $2 = \frac{k}{12}$ $2 = k/12$ => $k = 12 \cdot 2$ $k = 12*2$ => $k = 24$ $k=24$ .

Equation can be represented as $x = \frac{24}{y}$ $x = 24/y$ . So, when $y = 6$ $y = 6$ , we get $x = \frac{24}{6}$ $x = 24/6$ => $x = 4$ $x=4$

Answer 2 · 2016-07-09T15:57:12

$y = 4$ $y = 4$

Write as an inverse proportion first then make an equation by multiplying by k,

$y \propto \frac{1}{x} \Rightarrow y = \frac{k}{x} k = x \times y$ $yprop1/x " " rArr " " y = k/x " " k = x xx y$

Find the value of k.

$k = 2 \times 12 = 24$ $k = 2 xx 12 = 24$

$y = \frac{24}{x} \Rightarrow y = \frac{24}{6}$ $y = 24/x " "rArr " "y = 24/6$

$y = 4$ $y = 4$

You can now find any value of y or x if you are given the x or the y value.