**Our standard form to slope intercept form calculator is designed to simplify the conversion of linear equations from standard form (Ax + By = C) to slope-intercept form (y = mx + b). **

**For example, converting the standard form equation 3x - 2y = 6 to slope-intercept form becomes effortless with a calculator, yielding the result y = (3/2)x - 3.**

**5x + y = 15**

- Isolate y: y = -5x + 15
- Slope: -5, Y-Intercept: 15

**7x – y = 14**

- Isolate y: y = 7x – 14
- Slope: 7, Y-Intercept: -14

**10x + 5y = 20**

- Divide by 5:

- This gives us:
- 2x + y = 4 →
- y = -2x + 4
- Slope: -2, Y-Intercept: 4

## Standard Form to Slope Intercept Form Calculator

Standard Form | Slope-Intercept Form | Slope (m) | Y-Intercept (b) |
---|---|---|---|

2x + y = 4 | y = -2x + 4 | -2 | 4 |

3x – 2y = 6 | y = (3/2)x – 3 | 3/2 | -3 |

4x + 3y = 12 | y = -(4/3)x + 4 | -4/3 | 4 |

x – y = 1 | y = x – 1 | 1 | -1 |

6x + 2y = 8 | y = -3x + 4 | -3 | 4 |

5x + y = 15 | y = -5x + 15 | -5 | 15 |

7x – y = 14 | y = 7x – 14 | 7 | -14 |

10x + 5y = 20 | y = -2x + 4 | -2 | 4 |

8x – 4y = 16 | y = 2x – 4 | 2 | -4 |

9x + y = 27 | y = -9x + 27 | -9 | 27 |

12x + y = 24 | y = -12x + 24 | -12 | 24 |

15x – y = 30 | y = 15x – 30 | 15 | -30 |

11x + y = 22 | y = -11x + 22 | -11 | 22 |

13x + y = 39 | y = -13x + 39 | -13 | 39 |

## Standard Form to Slope Intercept Form Conversion Formula

Starting with the standard form equation **Ax + By = C**, where **A, B, and C** are constants and **B ≠ 0**, the conversion formula involves these steps:

- First, isolate all terms with ‘y’ on one side of the equation.
- Factor out ‘y’ from its terms.
- Divide all terms by the coefficient of ‘y’ (B).

The resulting formula transformation is:

- Standard Form:
**Ax + By = C** - Slope-Intercept Form:
**y = (-A/B)x + (C/B)**

Converting **4x + 2y = 8**:

- Subtract 4x from both sides:
2y = -4x + 8- Divide everything by 2:
y = -2x + 4

## How to Convert Standard Form to Slope Intercept?

Given the equation **6x – 3y = 12**:

- First, isolate terms with ‘y’:
**-3y = -6x + 12** - Divide all terms by -3:
**y = 2x – 4**

This process reveals both the **slope** (2) and the **y-intercept** (-4) in a clear format. The resulting equation shows that for every unit increase in x, y increases by 2 units, and the line crosses the y-axis at -4.

**Standard Form**: **2x + y = 6**

**Isolate y**on the left side: y =**-2x + 6**- The equation is now in slope-intercept form (y = mx + b) where:
**Slope (m)**=**-2****y-intercept (b)**=**6**

**Negative Terms**

- Get y by itself by subtracting
**3x**from both sides: -y =**-3x – 4** - Multiply all terms by
**-1**to solve for y: y =**3x + 4** - Final slope-intercept form shows:
**Slope (m)**=**3****y-intercept (b)**=**4**

### Fractional Coefficients

- Isolate y terms: 2y =
**-4x + 8** - Divide everything by
**2**: y =**-2x + 4** - Result shows:
**Slope (m)**=**-2****y-intercept (b)**=**4**

### Zero Terms

- Isolate y: -y =
**-x** - Multiply by
**-1**: y =**x** - In slope-intercept form:
**Slope (m)**=**1****y-intercept (b)**=**0**

## What is the symbol for slope-intercept form?

The slope-intercept form is universally represented as **y = mx + b**, where:

**m**represents the slope (rate of change)**b**represents the y-intercept (where the line crosses the y-axis)

This symbolic representation is powerful because it immediately conveys key information about the linear relationship.

For example, in **y = 3x + 5**:

- The slope (m) = 3, indicating a positive slope.
- The y-intercept (b) = 5, showing where the line crosses the y-axis.

## Writing Equations in Point-Slope Form

Point-slope form provides another way to express linear equations:

`Written as `**y - y₁ = m(x - x₁)**

**where:**

- (x₁, y₁) is a point on the line.
- m is the slope.

## References

- Purplemath – Linear Equation Forms https://www.purplemath.com/modules/stndform.htm
- Mathematics LibreTexts – Converting Between Forms https://math.libretexts.org/Bookshelves/Algebra/Elementary_Algebra

**Related Math Tools:**