### Build a linear function f knowing that the graph of f passes through the point (1;2) and (3;1) ?

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The linear function put in standard form is: f(x) = ax + b

Since the graph of the function is passing through the points (1,2) and (3,1), that means that if we'll substitute the coordinates of the points into the expression of the function, we'll get the relations:

f(1) = 2

f(1) = a*1 + b

a + b = 2 (1)

f(3) = 1

f(3) = 3a + b

3a + b= 1 (2)

We'll subtract (1) from (2):

3a + b -a - b = 1 - 2

We'll combine and eliminate like terms:

2a = -1 => a = -1/2

We'll substitute a in (1):

-1/2 + b = 2

b = 2 + 1/2

b = 5/2

The expression of the linear function is: f(x) = -x/2 + 5/2

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