Linear FunctionWhat is the linear function f if the graph of f passes through the point (1;3) and (2;1) ?

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ncchemist's profile pic

ncchemist | eNotes Employee

Posted on

The basic equation for a line is y = mx+b where m is the slope and b is the y-intercept.  First let's calculate the slope:

m = (y2-y1)/(x2-x1) = (3-1)/(1-2) = 2/-1 = -2

We can input the slope into the general equation to find the y-intercept:

y = mx + b = -2x + b

Input the first set of points (1,3):

3 = -2(1) + b

3 = -2 + b

b = 5

The equation of the linear function passing through both points given is:   y = -2x + 5. 

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

A linear function is determined when it's coefficients are determined.

y = f(x) = mx + n

So, in order to determine y, we'll have to calculate the coefficients m and n.

Since the function is determined by the points (1,3) and (2,1), 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) = 3

f(1) = m*1 + n

m + n = 3 (1)

f(2) = 1

f(2) = 2m + n

2m + n = 1 (2)

We'll subtract (1) from (2):

2m + n -m - n = 1 - 3

We'll combine and eliminate like terms:

m = -2

We'll substitute m in (1):

m + n = 3

-2 + n = 3

n = 3+2

n = 5

The expression of the linear function is:

f(x) = -2x + 5

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