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Annie's Attic does not have a proportional relationship but Bettie's Boutique does. The constant of proportionality at Betty's Boutique is 0.8.

Step-by-step explanation:

Step 1; To have a proportional relationship, if x's value varies, the y's value should also vary. If x increases, y increases correspondingly while if x decreases, y should also decrease.

Step 2; For Annie's Attic, the sale price = Original price - $5.

No matter what the value of the original price, there is only a difference of $5. Even if the price is increased to $100 the discount will only be $5. So this is not a proportional relationship.

Step 3; At Bettie's Boutique, they are having a 20% off sale. Whatever the cost, 20% is reduced. If bought for $15, price is $15 - 20% = $12. If bought for $25, the price will be $25 - 20% = $20.

If the original price is taken as x as the sale price is y, the relationship is given by; y = (100% - 20%) × x = 80% × x = 0.8 × x. So y = 0.8x. Here the constant of proportionality is 0.8.

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