anonymous
  • anonymous
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
Mathematics
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anonymous
  • anonymous
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
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • 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
  • freckles
does 6=12 or 9=18?

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anonymous
  • anonymous
idk
freckles
  • freckles
so you are not sure if 6 is the same number as 12 or not?
anonymous
  • anonymous
i think
freckles
  • freckles
or if 9 is the same number as 18 or not
freckles
  • freckles
9 and 18 aren't the same number 6 and 12 aren't the same number
freckles
  • freckles
I think you know that deep down
freckles
  • freckles
I think you would know the difference between 9 dollars and 18 dollars
freckles
  • freckles
or 6 dollars and 12 dollars
freckles
  • freckles
12 is more than 6 so they can't be equal 18 is more than 9 so they can't be equal
anonymous
  • anonymous
i thought it was like a trick Q or sumpthing
freckles
  • freckles
no 6=12 means 6 is 12 which you know is not true
freckles
  • freckles
so the other points on your table do not fit into the equation y=x
freckles
  • freckles
which means table 1 is not a direct variation
anonymous
  • anonymous
ok
freckles
  • freckles
ok again a direct variation is of the form y=kx where k holds constant
freckles
  • freckles
the first point listed on table 2 is (2,14)
freckles
  • freckles
find k such that (2,14) is on y=kx
freckles
  • freckles
just like I did before by pluggin in 14 for y and 2 for x
anonymous
  • anonymous
ok
freckles
  • freckles
14=k(2) or 14=2k can you solve this for k?
anonymous
  • anonymous
what is k
freckles
  • freckles
k is the constant of variation
freckles
  • freckles
k holds constant no matter what ordered pair (x,y) we have
anonymous
  • anonymous
i dont get it
freckles
  • freckles
if 14=2k then k=7
freckles
  • freckles
y=kx k=7 so the equation is y=7x
freckles
  • freckles
does equation hold for the other points on your table?
anonymous
  • anonymous
yes??
freckles
  • 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
  • freckles
|dw:1435880497051:dw||dw:1435880509906:dw|
freckles
  • 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
  • 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
  • anonymous
ok
freckles
  • freckles
any questions do you get it now ?
anonymous
  • anonymous
yes so the ans is
anonymous
  • anonymous
D
freckles
  • freckles
I gave you the answer above :p
freckles
  • freckles
no I did not say that at all
anonymous
  • anonymous
u did
freckles
  • freckles
I did not say D
anonymous
  • anonymous
where
freckles
  • freckles
|dw:1435880815810:dw||dw:1435880837282:dw|
anonymous
  • anonymous
so table 2 thanks
freckles
  • 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
  • anonymous
yes thanks
freckles
  • freckles
in order for k to be a constant by definition of constant it has to remain the same

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