Slope-Intercept to Standard Form Calculator
Convert a line from slope-intercept form (y = mx + b) into standard form (Ax + By = C) instantly. Handles fractions/decimals, shows steps, and lets you download results as CSV or PDF for sharing.
Developed by: Nohman Habib
Example Data
| Input (slope-intercept) | m | b | Output (standard form) |
|---|---|---|---|
| y = 2x + 3 | 2 | 3 | 2x - y = -3 |
| y = -3/4x + 2 | -3/4 | 2 | 3x + 4y = 8 |
| y = 0.5x - 1.25 | 1/2 | -5/4 | 2x - 4y = 5 |
Formula
Start with y = mx + b. Move the x-term to the left to get -mx + y = b. Then clear any fractions/decimals to make A, B, and C integers, and (optionally) reduce by the greatest common divisor so the coefficients are simplest.
How to Use This Calculator
- Enter an equation like y = 2x + 3, or enter m and b directly.
- Choose whether to force A positive and reduce coefficients by GCD.
- Click Calculate to see the standard form and step-by-step work above the form.
- Use Download CSV or Download PDF to save your results.
FAQs
1) What is standard form for a line?
Standard form is commonly written as Ax + By = C, where A, B, and C are typically integers.
2) Why do some answers look different but still correct?
You can multiply both sides of an equation by the same nonzero number without changing the line. That’s why 2x - y = -3 and -2x + y = 3 represent the same line.
3) Do A, B, and C have to be integers?
Not strictly, but many textbooks prefer integers. This calculator clears fractions/decimals so the final coefficients are integers.
4) What does “Force A positive” mean?
If the computed A is negative, the calculator multiplies the whole equation by -1 so A becomes positive (a common convention).
5) How does the calculator handle fractions like 3/4?
Fractions are treated exactly (as rational numbers). The calculator uses least common multiples to clear denominators and then simplifies the result.
6) What if the equation has no x term, like y = 5?
That’s a horizontal line with slope m = 0. In standard form it becomes 0x + y = 5, and the calculator will show that conversion.