Final answer:
To write a linear function with the points f(-4) = 2 and f(6) = -3, calculate the slope using the slope formula and use one point to find the y-intercept. The linear function is f(x) = -0.5x.
Step-by-step explanation:
To write a linear function f with given points f(-4) = 2 and f(6) = -3, you need to first determine the slope of the line. The slope (m) can be found using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) are the coordinates of the first point and (x2, y2) are the coordinates of the second point.
Plugging in our values, we get m = (-3 - 2) / (6 - (-4)) = (-5) / (10) = -0.5. Now that we have the slope, we can use one of the points to find the y-intercept (b) of the equation of the line in the form y = mx + b. Using the point (-4, 2), we can substitute into the equation to get 2 = (-0.5)(-4) + b, which simplifies to 2 = 2 + b. Subtracting 2 from both sides, we find that b = 0.
Therefore, the linear function that satisfies the two given points is f(x) = -0.5x.