Final answer:
The dependent variable in this scenario is the total cost of the membership, while the independent variable is the number of people on the membership. To find the rate of change (slope) and the initial value (y-intercept) of the linear equation, we can take any two points from the table and use them to calculate the slope and find the initial value.
Step-by-step explanation:
The dependent variable in this scenario is the total cost of the membership, while the independent variable is the number of people on the membership. The total cost of the membership depends on the number of people as shown in the table. Since the relationship between the two quantities is linear, we can find the equation that expresses the total cost in terms of the number of people.
To find the rate of change (slope) and the initial value (y-intercept) of the linear equation, we can take any two points from the table and use them to calculate the slope.
Let's say we choose two points, (x1, y1) and (x2, y2), from the table. The rate of change (slope) can be calculated using the formula:
slope = (y2 - y1) / (x2 - x1)
Once we have the slope, we can use one of the points, for example (x1, y1), and the slope to find the initial value (y-intercept) using the point-slope form of a linear equation:
y - y1 = slope(x - x1)
Substituting the values of the slope, x1, and y1 into the equation, we can find the initial value.