Final answer:
The function for the total amount charged for visits to the museum is f(x) = 50 + 15x, where 50 is the initial fee and 15 is the rate of change per visit. The slope of the line is 15, indicating the cost increases by $15 for each additional visit.
Step-by-step explanation:
The function for the total amount charged for x trips to the museum is given by f(x) = 50 + 15x, where 50 is the initial membership fee and 15 is the cost per visit. To create a table of ordered pairs (x, f(x)), you would list the number of visits next to the corresponding total amount charged. For example, if x = 1, then f(x) = 65.
The rate of change, or the slope of the line, in this context is 15. This is because the total cost increases by $15 for each additional visit. The slope of the function's graph represents this rate at which the total cost increases per visit. In this case, the graph would be a straight line starting from the y-intercept at (0, 50) and going upward with a slope of 15.To graph the function, we can plot the ordered pairs on a coordinate plane and connect them with a straight line. The rate of change, or slope, of the line is 15. This means that for every additional trip to the museum, the total amount charged increases by $15. The slope of the line reflects the relationship between the number of museum visits and the total amount charged.