Question

Indicate what variations occur by marking as follows:

A: Direct variation B: Inverse variation
C: Joint variation D: Combined Variation
E: No variation.

1. y=3x
2. xy=14
3. x^2=9
4. y=6xz
5. a=b/5
6. r=2s/t
7. x-1=10
8. 36=x/y

Can you explain the terms above to me so i can try and do these 8 question Please.

Answer 1

Direct variation: as the independent variable goes up, the dependent variable goes up. Likewise, this applies in the opposite direction: as the independent variable goes down, the dependent variable goes down.

Answer 2

So this means that direct variation is in the basic form


y = kx


for some constant k

Answer 3

So which equations do you see in this form?

Answer 4

Number one.

Answer 5

exactly

Answer 6

any others?

Answer 7

Number 4?

Answer 8

no, it's close though...the only problem is that there are 2 variables on the right side instead of 1

Answer 9

Oh, ok. I see that now.

Answer 10

can we rewrite any equations and get them into a more standard form?

Answer 11

Um, im not sure how to.

Answer 12

that matches y = kx

Answer 13

alright, notice that in #5, we're dividing by a scalar

Answer 14

since multiplication is the opposite of division, this means that we can represent b/5 as 1/5 times b

Answer 15

so in #5, a = b/5 turns into a = 1/5 times b

Answer 16

does that fit the form y = kx?

Answer 17

Oh ok. So that would make it a Direct variation?

Answer 18

yes you are correct

Answer 19

I dont think there is anymore, is there?

Answer 20

nope, we got them all and we can't rewrite any more into the form y = kx


so let's move onto inverse variation

Answer 21

inverse variation: as one variable goes up, the other goes down (or vice versa)

Answer 22

this can be represented in the general form


y = k/x

Answer 23

are there any equations that look like this

Answer 24

Number 8?

Answer 25

or number 4?

Answer 26

close, but now that I look at it more closely, you can rewrite #8 as

36 = x/y

36y = x

y = x/36

y = 1/36 times x

So #8 is a direct variation

Answer 27

# 4 is not an inverse variation because we're not dividing by any variables

Answer 28

Eh. This stuff is kind of confusing.

Answer 29

#6 is something that experiences inverse variation because notice how we're dividing by 't'

Answer 30

Thats the only one isnt it?

Answer 31

but there's more to the story as #6 also experiences direct variation (since there's a variable in the numerator)

Answer 32

because #6 has both direct and inverse variation, this means that #6 is representing Combined Variation

Answer 33

Which one would you pick?

Answer 34

I would pick Combined Variation because that's a better description (it tells us more about the equation)

Answer 35

so that would make #8 have Combined Variation as well (wasn't thinking about this one til just now)

Answer 36

now onto joint variation, this is variation that's direct but it can have 2 or more variables on the right side


So something like #4. y=6xz represents joint variation

Answer 37

thats the only one isnt it?

Answer 38

yes, it's the only one

Answer 39

Sorry I'm a bit all over the place with this solution. To clean things up, the answers are....


1. y=3x ....... direct

2. xy=14 ....... inverse (since we can rewrite into y = 14/x)

3. x^2=9 ....... no variation

4. y=6xz ....... joint

5. a=b/5 ...... direct

6. r=2s/t ....... combined

7. x-1=10 ..... no variation

8. 36=x/y ..... combined

Answer 40

let me know if this helps and feel free to ask about anything in particular

Answer 41

Thank you for helping. I have some more questions. If you can help me.

Answer 42

sure, post to the left to make a new thread

Answer 43

or if it's about these problems, then you can ask here

Answer 44

Ok.

Answer 45

let me know which option you're choosing

Answer 46

new thread

Answer 47

alright thanks