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
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