tell whether the table represents direct variation. if so, write the direct variation equation. show work that supports your conclusion. number of movie posters ordered                 total bill 2                                                               $14.93 3                                                                $20.42 5                                                               $31.40 9                                                               $53.36

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It does not represent direct variation. If we let `b` stand for the amount of the bill and `p` for the number of posters ordered, then we would have direct variation if and only if `b=kp` for some number `k`(which would represent the price of one poster).

But since `14.93=k*2,`...

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It does not represent direct variation. If we let `b` stand for the amount of the bill and `p` for the number of posters ordered, then we would have direct variation if and only if `b=kp` for some number `k`(which would represent the price of one poster).

But since `14.93=k*2,` which can simply be read off from the first line in the table, we would have `k=$7.465`. But then buying 9 posters should result in a price of `($7.465)(9)=$67.17` , which isn't the listed price. Therefore there can't be any such `k` and therefore no direct variation.

Maybe a more natural way to think about it is to realize that in direct variation, if the number of posters bought is multiplied by 3, so is the price. But 3 posters go for $20.42, while 9 go for only $53.36, which is not 3 times $20.42.

Either way, this doesn't represent direct variation.

 

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