The equation y = 2x - 48 represents y, the profit earned by the hot dog stand for x hot dogs sold. Hence, 3rd option is the right choice.
Equations are relations between two equal expressions, usually used to find the values of unknown variables using the constants and the values of other variables (if any).
In the question, we are informed that the profit earned by a hot dog stand is a linear function.
We are also informed that it costs the owner $48 each morning for the day's supply and that he earns $2 profit on each hot dog he sells.
We are asked to find the equation of profit y, for the number of hot dogs sold x.
The basic cost to the owner is $48. This will be his fixed cost, irrespective of the number of hot dogs he sells.
His profit on one hot dog is $2. So, his profit on x number of hot dogs sold will be $2x.
His total profit will be equal to the profits he earned by selling x hot dogs minus the basic cost he needs to pay.
∴ Profit earned = Profit on x hot dogs - Basic cost
or, y = 2x - 48.
∴ The equation y = 2x - 48 represents y, the profit earned by the hot dog stand for x hot dogs sold. Hence, 3rd option is the right choice.
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