Final answer:
The linear function is f(x) = (-2 / 3)x + 17 / 3, found by calculating the slope between two points and using the point-slope form.
Step-by-step explanation:
To find the equation of the linear function f(x), we use the two given points, (-1, 5) and (5, 1). First, calculate the slope using the formula slope (m) = (change in y) / (change in x). Thus, the slope is (1 - 5) / (5 - (-1)) = -4 / 6 = -2 / 3. Next, we use the point-slope form to write the equation: y - y1 = m(x - x1), and choose one of the points to substitute in.
Let's use (-1, 5): y - 5 = (-2 / 3)(x - (-1)), which simplifies to y - 5 = (-2 / 3)x - (2 / 3). Add 5 to both sides to get y = (-2 / 3)x + (2 / 3) + 5, which simplifies to f(x) = (-2 / 3)x + 17 / 3.