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Linear functionsBuild a linear function f knowing that the graph of f passes through...

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greynose | Student, Undergraduate | (Level 2) Honors

Posted May 25, 2011 at 12:13 AM via web

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Linear functions

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

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted May 25, 2011 at 1:05 AM (Answer #2)

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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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