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
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