If y varies inversely as x, and y=10 as x=7, how do you find y for the x-value of 10?

1 Answer
Don't Memorise
Jun 3, 2015

Inverse variation can be represented as:
# y = k/x#
# k = y.x#

where #color(green)(k# is the constant

# x = 7 and y = 10#
so ,
# color(green)(k = 7 xx 10 = 70#

Now, we have the value of #color(green)(k)# and #x = 10# , substituting these in the variation to find #color(red)(y#
#k= color(red)(y).x#

# color(red)(y )= k/x#

# color(red)(y = 70/10 = 7#

on observing the values

  • when # x = 7 , color(red)(y) = 10# , and
  • when # x = 10 , color(red)(y) =3#

as the value of #x# decreases #y# increases and vice verse as they vary inversely.

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