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

Question

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 · Answer

@freckles

freckles · Answer

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 · Answer

does 6=12 or 9=18?

anonymous · Answer

idk

freckles · Answer

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

anonymous · Answer

i think

freckles · Answer

or if 9 is the same number as 18 or not

freckles · Answer

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

freckles · Answer

I think you know that deep down

freckles · Answer

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

freckles · Answer

or 6 dollars and 12 dollars

freckles · Answer

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

anonymous · Answer

i thought it was like a trick Q or sumpthing

freckles · Answer

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

freckles · Answer

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

freckles · Answer

which means table 1 is not a direct variation

anonymous · Answer

ok

freckles · Answer

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

freckles · Answer

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

freckles · Answer

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

freckles · Answer

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

anonymous · Answer

ok

freckles · Answer

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

anonymous · Answer

what is k

freckles · Answer

k is the constant of variation

freckles · Answer

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

anonymous · Answer

i dont get it

freckles · Answer

if 14=2k
then k=7

freckles · Answer

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

freckles · Answer

does equation hold for the other points on your table?

anonymous · Answer

yes??

freckles · Answer

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|