1. What is the Standard Form Equation?

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers (usually), and A should be non-negative. This form is useful for analyzing and graphing linear equations.

2. How Does the Calculator Work?

The calculator uses the standard form equation:

Where:

• \( A \) — Coefficient of x (should be non-negative)
• \( B \) — Coefficient of y
• \( C \) — Constant term
• \( x \) — First variable (typically 'x')
• \( y \) — Second variable (typically 'y')

Explanation: The calculator simply combines your inputs into the standard form equation format.

3. Importance of Standard Form

Details: Standard form makes it easy to find x- and y-intercepts, is useful in systems of equations, and is the preferred form for many algebraic operations.

4. Using the Calculator

Tips: Enter the coefficients (A, B), constant (C), and variable names (x, y). The calculator will format them into standard form.

5. Frequently Asked Questions (FAQ)

Q1: Should A always be positive?
A: By convention, yes. If A is negative, multiply the entire equation by -1 to make it positive.

Q2: Can A, B, or C be fractions?
A: Yes, but standard form typically uses integers. You can multiply through by the denominator to eliminate fractions.

Q3: What's the difference between standard form and slope-intercept form?
A: Slope-intercept form is y = mx + b, which explicitly shows the slope and y-intercept, while standard form is better for certain calculations.

Q4: How do I find intercepts from standard form?
A: X-intercept: set y=0 and solve for x (x = C/A). Y-intercept: set x=0 and solve for y (y = C/B).

Q5: Can this be used for vertical or horizontal lines?
A: Yes. For horizontal lines (B=0): Ax = C. For vertical lines (A=0): By = C.