1. What is Standard Form to Slope Intercept Form Conversion?

This calculator converts linear equations from standard form (Ax + By + C = 0) to slope-intercept form (y = mx + b). The slope-intercept form is particularly useful for graphing and understanding the slope and y-intercept of a line.

2. How Does the Calculator Work?

The calculator uses the following conversion:

Where:

• \( A \) — Coefficient of x in standard form
• \( B \) — Coefficient of y in standard form
• \( C \) — Constant term in standard form
• \( m \) — Slope (-A/B)
• \( b \) — Y-intercept (-C/B)

3. Importance of Linear Equation Forms

Details: Different forms of linear equations are useful for different purposes. Standard form is good for finding intercepts, while slope-intercept form makes graphing straightforward.

4. Using the Calculator

Tips: Enter the coefficients A, B, and C from your standard form equation. B cannot be zero (would make it a vertical line).

5. Frequently Asked Questions (FAQ)

Q1: What if B is zero in standard form?
A: This represents a vertical line (x = constant) which cannot be represented in slope-intercept form.

Q2: Can I convert from slope-intercept to standard form?
A: Yes, by rearranging: y = mx + b → mx - y + b = 0.

Q3: What's the advantage of slope-intercept form?
A: It directly shows the slope and y-intercept, making graphing and analysis easier.

Q4: How do I handle fractions in the result?
A: The calculator provides decimal results, but you can convert to fractions if preferred.

Q5: What about horizontal lines?
A: Horizontal lines (y = constant) are a special case where A = 0 in standard form.