Final answer:
To write a linear function with the given values of f(-4) = 2 and f(6) = -3, we calculate the slope (m) as -0.5 and the y-intercept (b) as 0. The linear function is f(x) = -0.5x.
Step-by-step explanation:
To write a linear function with the given values, we need to find the slope (m) and the y-intercept (b).
Using the point-slope form of a linear equation, we can calculate the slope as:
m = (f(6) - f(-4)) / (6 - (-4))
Substituting the values f(6) = -3 and f(-4) = 2, we get:
m = (-3 - 2) / (6 - (-4)) = -5 / 10 = -0.5
Now, we can use the slope-intercept form of a linear equation to find the function:
f(x) = mx + b
Using the point (-4, 2), we can substitute the values for x and f(x) to solve for b:
2 = -0.5 * (-4) + b
Simplifying, we find:
2 = 2 + b
Subtracting 2 from both sides, we get:
b = 0
Therefore, the linear function is:
f(x) = -0.5x
Learn more about writing linear function