# The points (1,2), (2,-2) belong to the same line. Which is the equation of the line?

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If the given points belong to the line, that means that the line is passing through these points.

Let's note these points as A(1,2), B(2,-2)

The equation of the line which passes through 2 given points is:

(xB-xA)/(x-xA) = (yB-yA)/(y-yA)

Now, we'll substitute the coordinates of the points into the equation:

(2-1)/(x-1) = (-2-2)/(y-2)

1/(x-1) = -4/(y-2)

We'll cross multiplying and we'll get:

y-2 = -4x+4

We'll add 2 both sides:

y = -4x + 4 + 2

The equation of the line is:

**y = -4x + 6**

The points (x1,y1) and (x2,y2) lies (or belongs) to the line

y-y1 = {(y2-y1)/(x2-x1) }(x-x1).

Here (x1,y1) = (1,2) and (x2,y2) = (2,2).

So y-2 = [(-2-2)/(2-1)](x-1)

y-2= -4(x-1)

4x+y-2-4 = 0.

4x+y-6 = 0 is the line to which the given 2 points belong.