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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?
does 6=12 or 9=18?
so you are not sure if 6 is the same number as 12 or not?
or if 9 is the same number as 18 or not
9 and 18 aren't the same number 6 and 12 aren't the same number
I think you know that deep down
I think you would know the difference between 9 dollars and 18 dollars
or 6 dollars and 12 dollars
12 is more than 6 so they can't be equal 18 is more than 9 so they can't be equal
i thought it was like a trick Q or sumpthing
no 6=12 means 6 is 12 which you know is not true
so the other points on your table do not fit into the equation y=x
which means table 1 is not a direct variation
ok again a direct variation is of the form y=kx where k holds constant
the first point listed on table 2 is (2,14)
find k such that (2,14) is on y=kx
just like I did before by pluggin in 14 for y and 2 for x
14=k(2) or 14=2k can you solve this for k?
what is k
k is the constant of variation
k holds constant no matter what ordered pair (x,y) we have
i dont get it
if 14=2k then k=7
y=kx k=7 so the equation is y=7x
does equation hold for the other points on your table?
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|
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)
T1 is meant to say table 1 TB2 is meant to say table 2 if you weren't sure where my abbreviations came from
any questions do you get it now ?
yes so the ans is
I gave you the answer above :p
no I did not say that at all
I did not say D
so table 2 thanks
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
in order for k to be a constant by definition of constant it has to remain the same