Question

What's inverse and direct variation?

Answer 1

For example, force varies directly with mass; F = ma
And acceleration varies inversely with m, a = F/m

Formally, a variable or quantity y varies DIRECTLY with another variable/quantity x, if there is a constant k such that
y = kx

y varies INVERSELY with x if there is a constant k such that
y = k/x

Answer 2

Wow, you're really good at explaining. :)
See I'm having trouble with this little chart...

Answer 3

So suppose y is a function of h. Does it vary directly or inversely?

If it varies directly, then there exists a constant k so that
y = kh

Does there exist such a constant?

Answer 4

If you multiply x times y and always get the same number that is inverse variation.

Answer 5

(that's an equivalent statement, yes.)

But coming back to your problem ... is there a constant k such that
y = kh ?

Answer 6

If there is such a number k, then y/h = k.

Answer 7

If you divide y by x and always get the same number that's direct variation.

Answer 8

So which is the table you posted? Direct or Inverse?

Answer 9

JamesJ Direct variation right?

Answer 10

Oh sorry mertsj yeah i think its direct

Answer 11

Yes, and what is the constant k such that y = kh?

Answer 12

10?

Answer 13

yes, clearly.

Answer 14

Lol yes..

Answer 15

So the variables h and y show direct variation?

Answer 16

Yes, because there is a number k, a constant, such that
y = kh

Answer 17

(Technically we want k to be not zero, and here it is 10, which isn't zero so we're in the clear. Can you see why we wouldn't want k = 0?)

Answer 18

5 * 0 = 0
4 * 0 = 0
2 * 0 = 0

where is the variation?

Answer 19

Not so much....

Answer 20

Why does it need to be 0?

Answer 21

*not 0

Answer 22

In both cases, we're trying to describe how the variable x changes or impacts the variable y.

If y is directly proportional to x, then as x increases in magnitude, y increases in magnitude. You can see that with your example of y and h. As h increases, y increases; as h decreases, y decreases.

If y is inversely proportional to x, then the opposite occurs:
- as x increases, y decreases
- as x decreases, x increases

If you have y = kx and k = 0, then we have
y = 0x = 0.

So y doesn't change _at all_ as x changes. That defeats the purposes of describing how one variable changes with another. In this case with k = 0, y does not change as x changes. So it's not useful to describe x and y to as being directional proportional.

Answer 23

So x and y can't be described as being directional proportional.

Answer 24

if changes in x result in no change in y (or vice versa), no. We do not say in that case that the two variables are directly proportional.

(And I should have written in my last sentence above directly proportional, not 'directional')

Answer 25

Alright!
(Haha! I was gonna say...)

Answer 26

Thanks SO much... I'm a lost cause when it comes to math! :)

Answer 27

don't say that. it takes work, like everything smart. But the payoff is huge.

Answer 28

;-)

Answer 29

Sometimes...! ;)
And on top of that i probably have a teacher who knows less then i do... not even joking...
So that only helps me being a lost cause! :P