Given the values of a linear function f, what is the value of f(100) based on the provided table?

To determine the value of f(100) from a linear function based on the provided table, it is essential to understand the properties of linear relationships. A linear function can typically be expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept. By looking at the values provided in the table, one can calculate the slope using two points and then apply it to find the corresponding output for f(100).

For example, if the table provides coordinates (x₁, y₁) and (x₂, y₂), you can calculate the slope (m) as (y₂ - y₁) / (x₂ - x₁). With the slope known, you can select one of the points, substitute its x and y values into the equation, and solve for the y-intercept (b). After establishing the equation of the linear function, substituting 100 into the equation yields f(100).

In this question, if the result from your calculations yields 40, that indicates that when x equals 100, f(x) equals 40, aligning with the characteristics of the linear function depicted in the table. This demonstrates how the relationship maintained consistent changes