# 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...

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,` 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.