What is expression of linear function if its graph is passing through the points (-1,3) and (3,1)?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The equation of the line passing through the points (x1, y1) and (x2, y2) is given by ( y - y1) = [( y2 - y1)/(x2 - x1)]( x - x1)

As the line passes through ( -1 , 3) and (3 , 1) we can substitute the values we have to get :

( y - 3) = [( 1 - 3)/(3 + 1)]( x + 1)

=> 4( y - 3) = -2( x + 1)

=> 2y - 6 = -x - 1

=> 2y = -x + 5

=> y = -x/2 + 5/2

=> f(x) = -x/2 + 5/2

The required function is f(x)=  -x/2 + 5/2

 

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

The standard form of a linear function f(x) is:

f(x) = ax + b

or

y = mx + n, where m represents the slope of the line and n represents the y intercept.

In this case, the graph of the function is passing through the given points.

By definition, a point belongs to a curve if the coordinates of the point verify the equation of the curve.

 (-1,3) is on the line y = ax+b if and only if:

 

3 = a*(-1) + b

-a + b = 3 (1)

(3,1) belongs to the line y = ax+b if and only if:

1 = a*3 + b

3a + b = 1 (2)

We'll multiply (1) by 3:

-3a + 3b = 9 (3)

We'll add (3) to (2):

3a + b - 3a + 3b = 1 + 9

We'll eliminate like terms:

4b = 10

b = 5/2

From (1)=>a = b - 3

a = 5/2 - 3

a = -1/2

The function f(x) whose graph is passing through the given points is:

f(x) = -(1/2)*x + 5/2

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