Question: The profit earned by a hot dog stand is a linear function of the number of hot dogs sold. It costs the owner $48 dollars each morning for the day’s supply of hot dogs, buns and mustard, but he earns $2 profit for each hot dog sold. Which equation represents y, the profit earned by the hot dog stand for x hot dogs sold?
1. **State the problem:** We want to find the equation for the profit $y$ based on the number of hot dogs sold $x$.
2. **Identify the components:** The owner has a fixed cost of $48$ dollars each morning, which is a loss or expense, so this is a negative amount in the profit equation.
3. **Profit per hot dog:** The owner earns $2$ dollars profit for each hot dog sold, so the profit increases by $2$ for each $x$.
4. **Form the linear equation:** The profit $y$ is the total profit after subtracting the fixed cost:
$$y = 2x - 48$$
5. **Explanation:** The term $2x$ represents the profit from selling $x$ hot dogs, and $-48$ represents the fixed cost that reduces the profit.
6. **Check the options:**
- $y = 48x - 2$ (incorrect, reverses cost and profit per hot dog)
- $y = 2x - 48$ (correct)
- $y = 48x + 2$ (incorrect, cost is positive and profit per hot dog is wrong)
- $y = 2x + 48$ (incorrect, cost should be subtracted)
**Final answer:** $$y = 2x - 48$$