Identify which table shows a direct variation.
Table 1
x y
2 2
6 12
9 18
Table 2
x y
2 14
6 42
9 63
A.
Table 1
B.
Table 2
C.
Table 1 and Table 2
D.
Neither table

- anonymous

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- anonymous

@freckles

- freckles

ok do for direct variation we want this
y=kx
where k holds constant
so table one we have:
x y
2 2
6 12
9 18
---
this says when x=2 we have y=2 (amongst other stuff)
so
y=kx
2=k(2)
this implies k should be 1 if this list of order pairs is to be a direct variation
k=1
y=x
so y=x should hold for all the other points on your list if it is a direct variation
do you have y=x for each line of table 1?

- freckles

does 6=12 or 9=18?

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## More answers

- anonymous

idk

- freckles

so you are not sure if 6 is the same number as 12 or not?

- anonymous

i think

- freckles

or if 9 is the same number as 18 or not

- freckles

9 and 18 aren't the same number
6 and 12 aren't the same number

- freckles

I think you know that deep down

- freckles

I think you would know the difference between 9 dollars and 18 dollars

- freckles

or 6 dollars and 12 dollars

- freckles

12 is more than 6
so they can't be equal
18 is more than 9
so they can't be equal

- anonymous

i thought it was like a trick Q or sumpthing

- freckles

no 6=12 means 6 is 12
which you know is not true

- freckles

so the other points on your table do not fit into the equation y=x

- freckles

which means table 1 is not a direct variation

- anonymous

ok

- freckles

ok again a direct variation is of the form y=kx
where k holds constant

- freckles

the first point listed on table 2 is (2,14)

- freckles

find k such that (2,14) is on y=kx

- freckles

just like I did before by pluggin in 14 for y and 2 for x

- anonymous

ok

- freckles

14=k(2)
or
14=2k
can you solve this for k?

- anonymous

what is k

- freckles

k is the constant of variation

- freckles

k holds constant no matter what ordered pair (x,y) we have

- anonymous

i dont get it

- freckles

if 14=2k
then k=7

- freckles

y=kx
k=7
so the equation is
y=7x

- freckles

does equation hold for the other points on your table?

- anonymous

yes??

- freckles

so it is a direct variation
Table 1
x y
2 2
6 12
9 18
|dw:1435880449113:dw|
Table 2
x y
2 14
6 42
9 63
|dw:1435880472148:dw|

- freckles

|dw:1435880497051:dw||dw:1435880509906:dw|

- freckles

when I said holds constant
that is the same thing as saying it doesn't change; it is a number that remains the same through the multiplication (and I say multiplication because we are talking about direct variation)

- freckles

T1 is meant to say table 1
TB2 is meant to say table 2
if you weren't sure where my abbreviations came from

- anonymous

ok

- freckles

any questions
do you get it now ?

- anonymous

yes so the ans is

- anonymous

D

- freckles

I gave you the answer above :p

- freckles

no I did not say that at all

- anonymous

u did

- freckles

I did not say D

- anonymous

where

- freckles

|dw:1435880815810:dw||dw:1435880837282:dw|

- anonymous

so table 2 thanks

- freckles

yes
but do you see why?
x*k=y
where k remained the same in table 2
but k did not remain the same in table 1

- anonymous

yes thanks

- freckles

in order for k to be a constant
by definition of constant it has to remain the same

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