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
If
then
Using this formula we find that if
Explanation:
Given,
or
this is if and only if
Also, we know that if
then
this gives us our formula
Then consider when
then
# 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
# => 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
# y = 8 => 8 = 24/x #
# :. x=24/8 = 3 #