1. What is Standard Form of Linear Equation?

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers with no common factors (other than 1), and A is non-negative. This form is useful for analyzing intercepts and solving systems of equations.

2. How Does the Calculator Work?

The calculator uses the following formulas:

Where:

• \( (x_1, y_1) \) — First point coordinates
• \( (x_2, y_2) \) — Second point coordinates
• A, B, C — Coefficients of the standard form equation

Explanation: These formulas convert two points into the coefficients of the standard form equation by calculating the differences in y and x coordinates.

3. Importance of Standard Form

Details: Standard form is particularly useful for finding x and y intercepts quickly (by setting y=0 and x=0 respectively) and for solving systems of linear equations using elimination methods.

4. Using the Calculator

Tips: Enter the coordinates of any two distinct points on the line. The calculator will automatically compute the standard form equation. Ensure points are not identical.

5. Frequently Asked Questions (FAQ)

Q1: What if my points are vertical or horizontal?
A: The calculator handles all cases. Vertical lines (x = constant) will have B=0, horizontal lines (y = constant) will have A=0.

Q2: Why is my equation not simplified?
A: This calculator shows the direct computation. For simplified form, divide all terms by their greatest common divisor.

Q3: Can I use decimal coordinates?
A: Yes, the calculator accepts decimal inputs and provides decimal coefficients in the output.

Q4: What if the points are the same?
A: The calculator requires two distinct points to define a line. Identical points will result in an invalid equation (0 = 0).

Q5: How is this different from slope-intercept form?
A: Standard form can represent vertical lines (unlike slope-intercept) and is better for integer solutions and intercept analysis.