Standard Form to Slope Intercept Calculator
Convert between standard form (Ax + By + C = 0) and slope-intercept form (y = mx + b)
Linear Equation Converter
Coefficient of x
Coefficient of y
Constant term
Standard Form Equation
Slope-Intercept Form Result
Conversion steps:
1. Start with: x + y = 0
2. Solve for y: By = -1x - 0
3. Divide by B: y = -1.000x + 0.000
Example Conversions
Example 1: Standard → Slope-Intercept
Given: 2x + 3y - 6 = 0
Steps:
1. 3y = -2x + 6
2. y = -2/3 x + 2
Result: y = -0.667x + 2
Slope: -2/3, Y-intercept: 2
Example 2: Slope-Intercept → Standard
Given: y = 2x - 1
Steps:
1. -2x + y + 1 = 0
2. 2x - y - 1 = 0
Result: 2x - y - 1 = 0
Coefficients: A = 2, B = -1, C = -1
Form Comparison
Standard Form
Ax + By + C = 0
Good for: Systems of equations, general analysis
Slope-Intercept Form
y = mx + b
Good for: Graphing, finding slope and intercept
Quick Reference
Slope (m): Rate of change, rise over run
Y-intercept (b): Where line crosses y-axis
Vertical lines: No slope-intercept form (B = 0)
Horizontal lines: Slope = 0, form: y = b
Understanding Linear Equation Forms
Standard Form: Ax + By + C = 0
The standard form represents a linear equation where all terms are on one side of the equation. This form is particularly useful for solving systems of linear equations and performing algebraic manipulations.
Key Features:
- •A, B, C: Constant coefficients
- •Works for all lines: Including vertical lines
- •Symmetrical: Treats x and y equally
Slope-Intercept Form: y = mx + b
The slope-intercept form explicitly shows the slope and y-intercept of a line, making it ideal for graphing and understanding the geometric properties of linear relationships.
Key Features:
- •m: Slope (rate of change)
- •b: Y-intercept (where line crosses y-axis)
- •Easy graphing: Start at (0,b), use slope to find more points
Conversion Formulas
Standard → Slope-Intercept
Given: Ax + By + C = 0
If B ≠ 0:
• Slope: m = -A/B
• Y-intercept: b = -C/B
• Result: y = (-A/B)x + (-C/B)
Slope-Intercept → Standard
Given: y = mx + b
Rearrange to: mx - y + b = 0
• A = m
• B = -1
• C = b