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)#