What is the linear function that passes through the points (2,1) and (1,1)?

We'll write the form of a linear
function:

f(x) = ax + b

A
linear function is determined when it's coefficients are determined. So, we'll have to
determine the coefficients a and b.

Since the function is
determined by the points (2,1) and (1,1), that means that if we'll substitute the
coordinates of the points into the expression of the function, we'll get the
relations:

f(2) = 1

f(2) =
a*2 + b

2a +
b = 1
(1)

f(1) = 1

f(1) =
a+b

a + b = 1 (2)

We'll put
(1) = (2):

2a + b = a +
b

We'll combine and eliminate like
terms:

2a - a = b - b

a =
0

We'll substitute a in (2):

b
= 1

Since the expression of the function is:
f(x) = 1, the function is not linear, but
constant.