Final answer:
To find the linear function f(x), we calculate the slope with the given points, which is -6/7, and then use one of the points to find the y-intercept, which is 5/7. The resulting equation is f(x) = (-6/7)x + 5/7.
Step-by-step explanation:
To find an equation for the linear function f(x), we need to determine the slope and y-intercept using the given points: f(-5) = 5 and f(2) = -1. First, we calculate the slope using the formula:
slope = (change in y) / (change in x) = (f(2) - f(-5)) / (2 - (-5)) = (-1 - 5) / (2 + 5) = -6 / 7.
Now that we have the slope (-6/7), we can use one of the points to find the y-intercept. Using the point (-5, 5), the equation f(x) = mx + b becomes:
5 = (-6/7)(-5) + b
This simplifies to:
5 = 30/7 + b
b = 5 - 30/7 = 35/7 - 30/7 = 5/7.
The y-intercept is 5/7, thus the equation for f(x) is:
f(x) = (-6/7)x + 5/7.