Assume that y varies inversely as x. If y = -6 when x = -2, how do you find y when x = 5?

1 Answer
Apr 5, 2016

Answer:

At #x=5 "; "y=12/5 = 2 2/5#

Explanation:

This is a version ratios (ratios turn up all over the place).

Consider the example: #a/b=c/d => a=bxxc/d#

This is exactly what we have in this question.

Let #k# be a constant

#y=kxx1/x#

#color(green)(y=k/x)# ...................................(1)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine the value of "k)#

Given condition: at #y=-6" "x=-2#

Substituting in equation (1)

#" "-6=k/(-2)#

Multiply both sides by 2

#(-6)xx2=kxx 2/(-2)#

But #2/(-2)=-1#

#=>-12=-k#

So #k=+12#

Thus equation (1) becomes

#color(green)(y=12/x)#.................................(2)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

So at #x=5# we have:

#" "y=12/5 = 2 2/5#