Suppose y is inversely proportional to x. If y = 6 when x = 4, how do you find the constant of proportionality and write the formula for y as a function of x and use your formula to find x when y = 8?

2 Answers
Jul 31, 2017

If #y# is inversely proportional to #x#, and if #y=6# when #x=4#

then #underline(y=24/x)#.

Using this formula we find that if #y=8# then #underline(x=3)#

Explanation:

Given, #y# is inversely proportional to #x#

or #y prop x^(-1)#

this is if and only if

#y prop 1/x#

#<=>#

#y=1/x k#

Also, we know that if #y=6# when #x=4#

then

#6=1/4 k#

#<=># multiply both sides by #4#

#24=k# this is our constant of proportionality

#=>#

this gives us our formula

#y=24/x#

Then consider when #y=8#

then

#8=24/x#

#<=># multiply both sides by #x#

#8x=24#

#<=># divide both sides by #8#

#x=3#

Jul 31, 2017

# K = 24 #

# y = 24/x#

# x = 3 # when # y = 8 #

Explanation:

"y is inversely proportional to x":

# => y prop 1/x #
# :. y = K 1/x = K/x#

"If #y = 6# when #x = 4#, how do you find the constant of proportionality":

# => 6 = K/4 #
# :. K = 24 #

"write the formula for y as a function of x"

# K = 24 => y = 24/x#

"use your formula to find #x# when #y = 8#"

# y = 8 => 8 = 24/x #
# :. x=24/8 = 3 #