1. What is the Standard Form of a Linear Equation?

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

2. How Does the Calculator Work?

The calculator uses the standard form equation:

Where:

• A, B, C — Coefficients (real numbers)
• x, y — Variables

Calculations performed:

• Slope (m) = -A/B
• x-intercept = C/A (when A ≠ 0)
• y-intercept = C/B (when B ≠ 0)

3. Importance of Standard Form

Details: The standard form is useful because:

• It clearly shows both x and y intercepts
• It's the preferred form for solving systems of equations
• It can represent vertical lines (unlike slope-intercept form)
• It's used in many linear algebra applications

4. Using the Calculator

Tips: Enter coefficients A, B, and C. The calculator will display:

• The equation in standard form
• The slope of the line
• x and y intercepts

5. Frequently Asked Questions (FAQ)

Q1: Can A or B be zero in standard form?
A: Yes, but not both. If A=0, the line is horizontal. If B=0, the line is vertical.

Q2: How do I convert standard form to slope-intercept form?
A: Solve for y: y = (-A/B)x + (C/B)

Q3: Why is standard form preferred in some cases?
A: It can represent all lines (including vertical ones) and is better for integer solutions.

Q4: What if all coefficients are zero?
A: If A=B=C=0, it represents all points in the plane. If C≠0 while A=B=0, there's no solution.

Q5: How do I find parallel/perpendicular lines?
A: Parallel lines have the same A/B ratio. Perpendicular lines have A/B ratios that are negative reciprocals.