If y=9 when x=9, how do you find y when y=-27 given y varies inversely as x?

1 Answer
Jun 12, 2017

Answer:

#x = -3# when #y = -27#

Explanation:

Inversely: #y = k/x " or using proportions: " y_1/y_2 = x_2/x_1#

Using the two step method , find #k# given #y " and " x#:

#9 = k/9#

Multiply both sides by #9# to eliminate the denominator on the right:

#9 * 9 = k/9 * 9/1#

#81 = k#

Now fill in the equation using #k#:

#(-27)/1 = 81/x#

Find #x# by using the cross product: #-27x = 81#

Divide both sides by #-27: " "(-27x)/-27 = 81/-27#

#x = -3#

Using Proportions: # y_1/y_2 = x_2/x_1#

#9/-27 = x/9#

Use the cross product: #-27 x = 81#

Divide both sides by #-27: " " (-27x)/-27 = 81/-27#

#x = -3#