Let f(x) be linear

f(16)=-5
f(20)= -17

Find f(x)
Calculate f(12)

To find the equation of a linear function, we need the values of two points. We can use the given points and the formula for finding the equation of a line, which is y = mx + b, where m is the slope of the line and b is the y-intercept.

Given points:
(16, -5)
(20, -17)

First, we can find the slope (m):
m = (change in y) / (change in x) = (-17 - (-5)) / (20 - 16) = (-17 + 5) / 4 = -12 / 4 = -3

Now that we have the slope (m), we can use one of the given points to find the y-intercept (b).
Using the point (16, -5):
-5 = -3(16) + b
-5 = -48 + b
b = -5 + 48
b = 43

Therefore, the equation of the linear function f(x) is:
f(x) = -3x + 43

To calculate f(12), we substitute x = 12 into the equation:
f(12) = -3(12) + 43
f(12) = -36 + 43
f(12) = 7

Therefore, f(12) = 7.