If y varies inversely as x and y = 5 when x = 10, how do you find y when x = 2?

2 Answers
Aug 7, 2016

Answer:

#y=25#

Explanation:

#y=k/x# ;where #x# and #y# are variables and #k# is constant
or
#5=k/10#
or
#k=5(10)#
or
#k=50#
So Equation becomes #y=50/x#
When #x=2#
#y=50/2#
or
#y=25#

Aug 7, 2016

Answer:

The equation is #y=50/x#

At #x=2;" "y=25#

Explanation:

There is a relationship between #y" and "x#

Mathematically this is written as #y color(white)(.)alpha color(white)(.) 1/x#

The #alpha# is stating that a relationship exists but as yet it is not totally defined

,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let #k# be the constants of variation

Write #y color(white)(.)alpha color(white)(.) 1/x# as: #" "y=kxx 1/x" " ->" " y=k/x#

You find the value #k# by substituting the values for the known condition #(x,y)->(10,5)#

Thus we have:

#y=kxx 1/x" " ->" "5=k/10#

Multiply both sides by 10

#10xx5=cancel(10)xxk/(cancel(10))#

#=>k=50#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So the equation is:

#y=50/x#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Thus at #x=2# we have:

#y=50/2=25#