For the direct variation y = (3/4) when x = (1/8), how do you find the constant of variation and find the value of y when x = 3?

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Answer 1 · 2017-01-21T18:40:13

For direct variation #y=3/4# when #x=1/8# the constant of variation is #k=6#, and when #x=3# we have #y=18#.

If a variable y varies directly with a variable x, then y is proportional to x.

The statement y is proportional to x, is the same as y equals x times a constant k.

#y prop x <=> y=kx#

Then we can plug in the case we already know if #y=3/4# then #x=1/8#.

#=> 3/4=k1/8# So we need to solve for k

#<=> 8(3/4)=24/4=6=k# Multiply both sides by 8 and simplify

So, #k=6#

Then we have #y=6x#

so we plug in #x=3#

#y=6(3)=18#