Standard Form to Slope Intercept Form Calculator - Convert Linear Equations

Convert linear equations from standard form (Ax + By = C) to slope intercept form (y = mx + b) instantly with our free online calculator. Whether you're working on algebra homework, graphing linear functions, or studying coordinate geometry, our tool provides accurate conversions in seconds.

Standard Form to Slope Intercept Form

Convert Ax + By = C to y = mx + b format:

Enter coefficients for: Ax + By = C

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What is Standard Form to Slope Intercept Conversion?

The standard form to slope intercept form conversion is essential for:

  • Graphing linear equations easily
  • Finding slope and y-intercept quickly
  • Algebra homework and test preparation
  • Understanding linear function properties
  • Coordinate geometry problems

Simply enter the coefficients A, B, and C from your standard form equation, and we'll instantly convert it to slope intercept form. No registration required - completely free to use!

How to Convert Standard Form to Slope Intercept Form

To convert from standard form (Ax + By = C) to slope intercept form (y = mx + b):

  1. Start with: Ax + By = C
  2. Subtract Ax from both sides: By = -Ax + C
  3. Divide by B: y = (-A/B)x + (C/B)
  4. Simplify: y = mx + b where m = -A/B and b = C/B

Note: If B = 0, the line is vertical and has an undefined slope.

Example Conversion

Converting 3x + 2y = 6

Step-by-step conversion process

Calculation: 2y = -3x + 6 → y = (-3/2)x + (6/2) → y = -1.5x + 3
Result: Slope (m): -1.5, Y-intercept (b): 3

Common Standard Form Examples

2x + 3y = 12 → y = -0.67x + 4
5x - 2y = 10 → y = 2.5x - 5
x + y = 5 → y = -x + 5
4x = 8 → x = 2 (vertical line)

Why Use Our Standard Form to Slope Intercept Calculator?

  • Instant conversion with no calculation errors
  • Handles all types of linear equations
  • Shows step-by-step results (slope, y-intercept, equation)
  • Works with decimal coefficients
  • Completely free and no registration required
  • Mobile-friendly and easy to use

Frequently Asked Questions (FAQ)

What is the difference between standard form and slope intercept form?

Standard form is written as Ax + By = C, while slope intercept form is y = mx + b. Standard form is useful for finding intercepts, while slope intercept form makes it easy to identify the slope and y-intercept directly.

Can all linear equations be converted from standard form to slope intercept form?

Most linear equations can be converted, but vertical lines (where B = 0) cannot be written in slope intercept form because they have an undefined slope. For example, x = 5 is a vertical line that cannot be expressed as y = mx + b.

What if the coefficient B is negative in standard form?

If B is negative, the conversion process remains the same. For example, 2x - 3y = 6 becomes y = (2/3)x - 2. The negative B simply affects the signs in the final slope intercept form.

How do I know if my conversion is correct?

You can verify your conversion by checking that both forms represent the same line. Pick any point that satisfies the original equation and verify it also satisfies the converted equation. Our calculator handles this verification automatically.

What should I do if I get fractions in my slope intercept form?

Fractions are perfectly normal and often unavoidable in slope intercept form. For example, 3x + 4y = 12 becomes y = -0.75x + 3. You can leave them as decimals or convert to fractions like y = (-3/4)x + 3.

Can I convert from slope intercept form back to standard form?

Yes, you can convert back by rearranging the equation. For y = 2x + 3, you would subtract 2x from both sides to get -2x + y = 3, or multiply by -1 to get 2x - y = -3.

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