Final answer:
The linear equation that defines the rule for the given table is f(x) = -2x + 46, which correctly matches the data when the calculated f(x) values for the given x values are compared to the table.
Step-by-step explanation:
To complete the linear equation that defines the rule for the given table with values of x and f(x), let's analyze the data provided. We observe that as x increases by 1, f(x) decreases by 2. This indicates that the slope of the line (m) is -2. We can use the point-slope form to write the equation of the line y - y1 = m(x - x1), where (x1, y1) is a point from the table. Choosing the point (3, 40), the equation becomes f(x) - 40 = -2(x - 3).
Simplifying, f(x) = -2x + 46 is the linear equation that represents the data.
To verify the equation, plug in the values of x from the table and check if they yield the corresponding f(x) values:
- For x = 3, f(x) = -2(3) + 46 = 40,
- For x = 4, f(x) = -2(4) + 46 = 38,
- For x = 5, f(x) = -2(5) + 46 = 36,
- For x = 6, f(x) = -2(6) + 46 = 34.
Each calculation matches the provided data, confirming that our equation is accurate.