Final answer:
The equation that represents the relationship between the number of packs of sodas Dwayne purchased and the total cost is y = 2.85x, indicating a direct proportionality between packs and cost.
Step-by-step explanation:
The student has provided information about a purchase Dwayne made and wants to know the equation that represents the relationship between the number of packs of sodas purchased (x) and the total cost for the sodas (y).
Given that Dwayne purchased 4 packs of sodas for a total of $11.40, we can find the cost per pack by dividing the total cost by the number of packs. This gives us $11.40 / 4 = $2.85 per pack. Therefore, the equation that represents this relationship is y = 2.85x, where 'y' is the total cost for 'x' number of packs of sodas.
If Dwayne were to buy more packs at the same price per pack, we would multiply the number of packs by the price per pack to find the total cost. The key concept here is that of a linear relationship, as the total cost is directly proportional to the number of packs purchased. This type of equation is often referred to as a linear equation or a direct variation, where the cost per pack is constant.