Standard Form to Slope Intercept Calculator

Estimate function values near a point using tangent line linearization. Perfect for quick approximations and understanding differentials.

Conversion Formula: If B ≠ 0, then y = (-A/B)x + (C/B). Slope m = -A/B, y‑intercept b = C/B.

If B = 0, the line is vertical: x = C/A (cannot be written in slope-intercept form).

Enter any real numbers. Use negative values where needed.
2x + 3y = 6
x - 2y = 4
y = 2 (0x+1y=2)
x = 3 (1x+0y=3)
3x + 4y = 12
-2x + 5y = 10
Conversion Results
1. Original Equation (Standard Form)
2x + 3y = 6
2. Slope-Intercept Form (y = mx + b)
y = -0.6667x + 2
Slope (m)
-0.6667
= -2/3
y-intercept (b)
2
= 2/1
x-intercept
3
= 3/1
3. Step-by-Step Conversion
Start: 2x + 3y = 6
Subtract 2x: 3y = -2x + 6
Divide by 3: y = (-2/3)x + 2
Line: Ax + By = C
Intercepts (hover for details)

Understanding Standard Form and Slope-Intercept Form

The standard form of a linear equation is Ax + By = C, where A, B, and C are real numbers, and A and B are not both zero. The slope-intercept form is y = mx + b, where m is the slope and b is the y‑intercept.

Conversion:

If B ≠ 0, isolate y:    y = - (A/B) x + (C/B).   So m = -A/B, b = C/B.

If B = 0, the equation becomes Ax = C → x = C/A (vertical line).

Key Properties

FormEquationSlopeIntercepts
StandardAx + By = C-A/B (B≠0)x-int: C/A, y-int: C/B
Slope-Intercepty = mx + bmy-int: b, x-int: -b/m

Applications

  • Graphing: Slope-intercept form makes it easy to plot the y‑intercept and use slope.
  • Systems of equations: Standard form is often used in elimination methods.
  • Modeling: Different contexts favor different forms (e.g., standard for integer coefficients).

Calculator features:

  • Real-time conversion as you type (or click "Convert")
  • Handles horizontal lines (B≠0, A=0) and vertical lines (B=0)
  • Shows exact fractions when possible (using nerdamer simplification)
  • Interactive graph with intercept points

Frequently Asked Questions

If A = 0 and B = 0, the equation is 0 = C, which is only valid if C = 0 (trivially true) or impossible. The calculator will show an error message.

Yes, you can enter decimal numbers. For exact fraction representation, you may multiply through by a denominator, but the calculator will show decimal approximations. Use the step‑by‑step to see rational expressions.

The graph displays the line corresponding to Ax+By=C. Red points mark the x‑ and y‑intercepts if they lie within the current view. You can adjust the range.