SOLUTION: In the equation: y=2/x x and y vary directly. True False

Question 80081: In the equation:
y=2/x
x and y vary directly.
True
False

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
False
.
If x and y vary directly, then as one of them increases, the other must increase also.
(or as one of them decreases, the other must decrease also).
.
This means that x cannot be in the denominator unless y is also in a denominator.
.
Think about this. Let's say that x = 1. Then the given equation becomes:
.
y = 2/x = 2/1 = 2
.
Now let's increase x by saying that x is going to be 2. If y varied directly as x then
because we increased x, y should also increase. But when we substitute 2 for x, the
equation becomes:
.
y = 2/x = 2/2 = 1
.
Notice that when x went from 1 to 2, the value of y went down from 2 to 1. So y does not
vary directly as x. It varies inversely ... the bigger x gets the smaller y gets.
.
Hope this helps you to understand the problem a little better. And sometimes it helps
just to plug numbers in and see what happens to one of the variables if you increase
(or decrease) the other one ... just as we did above.
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