Final answer:
The slope of the cost function for the carnival games is the cost per game, which is $0.75. There is no fixed cost or starting fee mentioned, so no further calculations are needed to find the slope. In other contexts, a negative slope may represent the opportunity cost of choosing between two goods.
Step-by-step explanation:
To find the slope of the cost function represented by playing games at the carnival, we first note the total cost and the cost per game. The total cost for the day was $11.50 after playing 11 games, with each game costing $0.75. To calculate the slope, we set up a linear equation in the form of y = mx + b, where y represents the total cost, m represents the slope (cost per game), x represents the number of games, and b is the starting value or fixed cost.
Here, since there is no mention of an initial fee or starting cost (meaning the cost starts at $0 when 0 games are played), the slope is simply the cost per game. Thus, the slope m is $0.75.
Alternatively, you may encounter situations where the algebraic sign of the slope is negative, indicating an inverse relationship between two goods. In such cases, the slope could be given as the opportunity cost, which is the ratio of the two prices involved. For instance, if bus tickets cost $0.50 each and burgers cost $2 each, the slope would be $0.50/$2 = 0.25. However, for this specific question, there is no inverse relationship mentioned, and thus the slope remains positive and equal to the cost per game.