1. What is the Standard Form Formula?

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), A is non-negative, and A, B, and C are integers when the equation is written in standard form.

2. How Does the Calculator Work?

The calculator uses the standard form equation:

Where:

• \( A \) — Coefficient of x (must be non-negative)
• \( B \) — Coefficient of y
• \( C \) — Constant term
• \( x \) — x variable (optional for solving)
• \( y \) — y variable (optional for solving)

Explanation: The calculator can either display the equation in standard form or solve for one variable when the other is provided.

3. Importance of Standard Form

Details: The standard form is useful for finding intercepts quickly (x-intercept when y=0, y-intercept when x=0) and is often used in systems of equations.

4. Using the Calculator

Tips: Enter coefficients A, B, and C. To solve for a variable, leave either x or y blank and provide a value for the other variable.

5. Frequently Asked Questions (FAQ)

Q1: Why is A required to be non-negative?
A: This is part of the standard form convention to maintain consistency in how equations are written.

Q2: Can A or B be zero?
A: Yes, but not both. If A=0, it's a horizontal line. If B=0, it's a vertical line.

Q3: How do I convert from slope-intercept to standard form?
A: Move all terms to one side of the equation so it's in the form Ax + By = C.

Q4: What's the advantage of standard form?
A: It's useful for solving systems of equations and clearly shows intercepts.

Q5: Can this calculator handle fractions?
A: Yes, you can enter decimal values for any of the coefficients or variables.