Suppose y varies inversely with x. How do you write an equation for the inverse variation for Y = 4 when x = 2.5?

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Answer 1 · 2016-05-16T09:21:42

$y=10/x" "larr" "4=10/2.5$

Varies inversely $" "->" "y=k/x$

Where $k$ is the constant of variation (conversion factor)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$color(purple)("Determine the value of "k)$

Using the given condition:

$color(brown)(" "y=k/xcolor(blue)(" "->" "4=k/2.5))$

Multiply both sides by $2.5$

$" "4xx2.5=kxx 2.5/2.5$

But $2/5/2.5=1$

$" "k=10$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$color(brown)(" "y=k/xcolor(blue)(" "->" "y=10/x)$