If y=-6.3 when x=2/3, how do you find y when x=8 given that y varies inversely as x?

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Answer 1 · 2017-06-06T12:45:35

$y=-21/40$

Given that $" "y=kxx1/x" "$ where $k$ is the constant of variation.

Known condition:

$y" "=" "kxx1/x" "->" "-6 3/10" "=" "kxx1/(2/3)$

$" "->" "-63/10" "=" "kxx3/2$

Multiply both sides by $2/3$

$" "->" "-63/10xx2/3" "=" "kxx1$

But 2 will divide exactly into 10 by 5 and 3 will divide exactly into 63 by 21 giving:

$" "->" "-(cancel(63)^(21))/(cancel(10)^5)xx(cancel(2)^1)/(cancel(3)^1)" "=" "k$

So $k=-21/5$

Thus we have: $" "y=-21/5xx 1/x" "->" "y=-21/(5x)$
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Let $x=8$ giving:

$y=-21/(5xx8)=-21/40$