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

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