## General Form Equation Calculator

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.

## What is the General Form Linear Equation?

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

How calculate the General Form Linear Equation from two coordinates (x_{1},y_{1}) and (x_{2},y_{2}).

Step 1: Calculate the slope (m) from the coordinates (y_{2 }- y_{1}) / (x_{2} - x_{1}). 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