Final answer:
The independent variable is the number of students and the dependent variable is the cost of dinner. The rate of change is 14, indicating that for every additional student, the cost of dinner increases by $14.
Step-by-step explanation:
The independent variable in this linear relationship is the number of students (x) and the dependent variable is the cost of dinner (y).
To find the rate of change, we can use the formula:
Rate of change = (change in y) / (change in x)
Let's calculate it using the given information:
For three students, the cost of dinner is $42, and for seven students, the cost is $98.
Change in x = 7 - 3 = 4
Change in y = 98 - 42 = 56
Rate of change = 56 / 4 = 14
Therefore, the rate of change for this situation is 14, indicating that for every additional student, the cost of dinner increases by $14.