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General Form Linear Equation Calculator

Calculate the General Form equation of a line (Ax + By + C = 0) with this General Form Linear Equation Calculator.

Coordinates of Point 1 (x1,y1): x= y=

Coordinates of Point 2 (x2,y2): x= y=

Fill in the coordinates of two points to find the linear equation in
(Ax + By + C = 0) form.

What is the General Form Linear Equation?

General Form Linear Equation: (Ax + By + C = 0)

To calculate the General Form Linear Equation from two coordinates
(x1,y1) and (x2,y2):

Step 1: Calculate the slope (m) from the coordinates: (y2 - y1) / (x2 - x1)
and reduce the resulting fraction to the simplest form.

Step 2: From the slope, calculate variables A and B with the equation:
Slope = - A / B

Step 3: Calculate the variable C by applying one of the coordinates to
the equation: Ax + By = -C

Result: Now you have calculated all three variables (A, B and C) for the
General Form Linear Formula.

Example:

To calculate the General Form Linear Equation for a line that includes
the two points ( -3, -1) and (3, 2).

Step 1: Determine the slope (m) : y2-y1 / x2-x1
(2 - -1) / (3 - -3)= 3/6 = 1/2

Step 2: From the slope, calculate variables A and B with the equation:
Slope = - A / B:

1/2 = - A / B

A = -1, B = 2

Step 3: Calculate the variable C to by applying one of the coordinates
(3, 2) to the equation: Ax + By = -C

-1x + 2y = -C
-3 + 4 = -C

1 = -C

C = -1

Result: The General Form Line Equation for coordinates ( -3, -1) and (3, 2)
is: -1x + 2y - 1 = 0

A = -1, B = 2, and C = -1

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