If f(x) is a linear function, then
f(x) = ax + b
for some constants a and b.
Given that f (1) = 4 and f (4) = 1, these constants are such that
f (1) = a + b = 4
f (4) = 4a + b = 1
Solve for a and b : eliminate b by subtracting the two equations,
(a + b) - (4a + b) = 4 - 1
-3a = 3
a = -1
Then
-1 + b = 4
b = 5
So we have
f(x) = -x + 5
