Calculate the General Form Equation of a line (Ax + By + C = 0) with this General Form Linear Equation Calculator. The calculator will present you with all three variables for the General Form Equation.

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

How 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). Then reduce the resulting fraction to the simplest form.

Step 2: From the slope, calculate variables A and B with this 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