Final answer:
The rate of change in this situation refers to how the total cost of the birthday party changes with respect to the number of people attending. The rate of change is $7 per person, and the equation that expresses the total cost in terms of the number of people attending is y = 7x + 250.
Step-by-step explanation:
The rate of change in this situation refers to how the total cost of the birthday party changes with respect to the number of people attending. In this case, the fixed cost is $250 to rent the facility, and there is an additional cost of $7 per person.
To find the rate of change, we can use the formula for a linear equation, y = mx + b, where y represents the total cost, m represents the rate of change, x represents the number of people attending, and b represents the fixed cost.
In this situation, the rate of change (m) is $7, as it is the cost per person. The fixed cost (b) is $250.
So the equation that expresses the total cost in terms of the number of people attending is y = 7x + 250.