To write a linear function, we need to determine the equation in the form y = mx + b, where m represents the slope and b represents the y-intercept.
Given that f(2) = -2 and f(1) = 1, we can substitute these values into the equation.
Substituting f(2) = -2:
-2 = 2m + b (equation 1)
Substituting f(1) = 1:
1 = m + b (equation 2)
Now we have a system of equations with two variables, m and b. We can solve this system by eliminating one of the variables.
Subtracting equation 2 from equation 1:
-2 - 1 = (2m + b) - (m + b)
-3 = m
Now we have found the value of m, which is -3. We can substitute this value back into equation 2 to find b:
1 = (-3) + b
b = 4
Therefore, the linear function is:
f(x) = -3x + 4