SOLUTION: Direct, inverse, or joint variation? Please Help. I really don't know the difference. {{{1/3}}}{{{Y=X}}} {{{xy=10}}}

Algebra ->  Expressions-with-variables -> SOLUTION: Direct, inverse, or joint variation? Please Help. I really don't know the difference. {{{1/3}}}{{{Y=X}}} {{{xy=10}}}      Log On


   

Question 162639This question is from textbook saxon algebra2
: Direct, inverse, or joint variation?
Please Help. I really don't know the difference.
1%2F3Y=X
xy=10 This question is from textbook saxon algebra2

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

It can't be joint, for there has to be more than two variables
to have joint variation.

To tell whether it is direct or inverse:

Substitute any two different values for X and calculate the two 
different values of Y for each.

If when X INcreases, Y also INcreases, and
when X DEcreases, Y also DEcreases then the variation is DIRECT.
(they go up or down in the SAME direction),

If when X INcreases, Y DEcreases, and
when X DEcreases, Y INcreases then the variation is INVERSE.
(they go up and down in OPPOSITE directions),

1%2F3Y=X

Substitute Y = 3:

1%2F3%283%29=X

1%2Fcross%283%29cross%283%29=X

X=1

Substitute Y = 6:

1%2F3%286%29=X
 
  2
1%2Fcross%283%29cross%286%29=X

X=2

So when X INcreased from 3 to 6, Y also INcreased
from 1 to 2, so the variation is DIRECT. 
(They both went UP).

----------------------- 

xy=10

Substitute x = 2:

%282%29y=10

y=5

Substitute x = 5:

%285%29y=10
 
y=2

So when X INcreased from 2 to 5, Y DEcreased
from 5 to 2, so the variation is INVERSE.
(One went up and the other went down).

Edwin