To determine the equation that represents the profit [tex]\( y \)[/tex] earned by a hot dog stand for selling [tex]\( x \)[/tex] hot dogs, we need to take into account two main factors:
1. The fixed cost the owner spends each morning for the day's supply.
2. The profit earned for each hot dog sold.
### Step-by-Step Solution:
1. Fixed Cost:
The owner spends \[tex]$48 each morning for the supplies. This can be considered a fixed cost, no matter how many hot dogs are sold. Therefore, this is a fixed deduction from the total revenue obtained.
2. Profit per Hot Dog:
For each hot dog sold, the owner earns \$[/tex]2 in profit. If [tex]\( x \)[/tex] is the number of hot dogs sold, then the total profit earned from selling these hot dogs is [tex]\( 2x \)[/tex].
3. Total Profit Calculation:
The total profit [tex]\( y \)[/tex] is obtained by subtracting the fixed cost from the total revenue earned by selling the hot dogs.
[tex]\[
\text{Revenue from hot dogs} = 2x
\][/tex]
[tex]\[
\text{Fixed cost} = 48
\][/tex]
The equation representing the profit:
[tex]\[
y = \text{Total Revenue} - \text{Fixed Cost}
\][/tex]
Substituting the known values:
[tex]\[
y = 2x - 48
\][/tex]
Given these steps, the equation that correctly represents the profit [tex]\( y \)[/tex] for selling [tex]\( x \)[/tex] hot dogs is:
[tex]\[ y = 2x - 48 \][/tex]
Therefore, the correct answer among the given choices is:
[tex]\[ \boxed{y = 2x - 48} \][/tex]
