Find the equation for the line passes through (1,3) and (2,-1)

Let's approach the problem in this way: If a point belongs
to a line, that means that the coordinates of the point verifies the equation of the
line.

Let's put the equation of the line in the standard
form:

y = ax + b

The point
(1,3) is on the line if and only if the coordinates verify the equtaion of the
line:

3 = a*1 + b (1)

The
point (2,-1) is on the line if and only if the coordinates verify the equtaion of the
line:

-1 = a*2 + b (2)

From
(1), we'll get a = 3-b (3)

We'll re-write (2) and
we'll substitute (3) in (2):

-1 = a*2 +
b

2a + b = -1

2(3-b) + b =
-1

We'll remove the
brackets:

6 - 2b + b + 1 =
0

We'll combine like
terms:

7 - b = 0

We'll add b
both sides:

 b =
7

a = 3-b

a =
3-7

a =
-4

The equation of the line
is:

y = -4x +
7