Final answer:
The tax on an item being directly proportional to the price of the item means we can represent the relationship with the equation y = 1.05x, where y represents the total cost and x represents the original price of the item.
Step-by-step explanation:
The tax on an item is directly proportional to the price of the item. This means that if the price of the item increases, the tax on it will also increase by an amount proportional to the initial price. To model this relationship, we're given that a $4.80 item has a total cost of $5.04. To find the equation that models this relationship, where the cost is represented by y and the price of the item is represented by x, we calculate the proportion of tax added to the original price.
Here’s how it's done:
- The difference between the total cost and the price of the item represents the tax, which is $5.04 - $4.80 = $0.24.
- To find the rate of tax, divide the tax amount by the price of the item: $0.24 / $4.80 = 0.05.
- The tax rate is thus 0.05, and the equation for the cost of an item including tax is y = 0.05x + x or y = 1.05x.
However, the equation you have provided does not match the context of this question. Be sure to analyze the problem and equations carefully.