Assume that y varies inversely as x. If x = 12 when y = 9, what is x when y = -3?

1 Answer
Oct 4, 2016

Answer:

#x = -36#

Explanation:

The basic inverse variation equation is

#xy = k#

where #k# is the constant of variation. In order to write the equation that reflects this relationship, we must find #k#. We use the known relationship of #x = 12# and #y = 9# to find #k#. Substituting in the basic equation, we will find #k#:

#xy = k#

#(12)(9) = k#

#108 = k#

This then yields the equation which relates #x# and #y#:

#xy = 108#

Now, use this equation and substitute the second value of #y# in order to find its related value of #x#:

#xy = 108#

#x(-3) = 108#

#x = 108/(-3)#

#x = -36#