Math
Standard Form to Slope Intercept Form Calculator
Convert Ax + By = C (or Ax + By + C = 0) to y = mx + b, or go the other way and clear fractions to get integer standard form. mathcheck shows the slope and both intercepts as exact fractions and lists every step of the rearrangement.
Coefficient of x.
Coefficient of y. B = 0 gives a vertical line.
Constant term.
Try an example
Result
Converted equation
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- Alternate form
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- Slope m
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- Y-intercept
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- X-intercept
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- Other forms
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Student quick launch
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Study path
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Standard form and slope-intercept form
Standard form Ax + By = C lists integer The number multiplying a variable, like the 3 in 3x. with x and y on the same side; it is convenient for A point where a graph crosses an axis. and for solving systems. How steep a line is: how much y changes for each step right in x.-intercept form y = mx + b isolates y so the slope m and y-intercept b can be read directly. Any non-vertical line can be written both ways.
Conversion recipes
| Direction | Steps | Example |
|---|---|---|
| Standard → slope-intercept | Subtract Ax, divide every term by B, reduce fractions | 2x + 3y = 12 → 3y = -2x + 12 → y = (-2/3)x + 4 |
| Slope-intercept → standard | Multiply by the denominator of m, move the x-term left, make A positive | y = (2/3)x - 4 → 3y = 2x - 12 → 2x - 3y = 12 |
| General Ax + By + C = 0 | Same as standard form, but move C to the right side first | 2x - 4y + 8 = 0 → 2x - 4y = -8 → x - 2y = -4 → y = (1/2)x + 2 |
How to use this calculator
- Pick the direction: standard form to slope-intercept, or slope-intercept to standard.
- For standard form, choose whether your equation is written Ax + By = C or Ax + By + C = 0, then enter A, B, and C.
- For slope-intercept form, type the slope as a fraction or decimal and the y-intercept b.
- Read the converted equation, the slope and intercepts, and the other forms of the same line.
- Open Show the work to see each rearrangement step.
How to read the answer
In the converted slope-intercept equation, m = -A/B is the slope and b = C/B is the y-intercept. Going the other way, the integer standard form Ax + By = C has x-intercept C/A and y-intercept C/B. Both equations describe exactly the same line, so any point that satisfies one satisfies the other.
Common mistakes and edge cases
- Dividing only the x-term by B. Every term, including the constant, must be divided.
- Dropping the sign of A when moving the x-term across the equals sign: 2x + 3y = 12 becomes 3y = -2x + 12.
- Forgetting to multiply the constant b by the The bottom number of a fraction; it says how many equal parts make one whole. when clearing the fraction from y = (2/3)x - 4.
- B = 0 means the line is vertical (x = C/A) and has no slope-intercept form.
- A slope written as a rounded decimal (0.33) will not produce clean integer coefficients; use the fraction 1/3.
Worked examples
Standard to slope-intercept
2x + 3y = 12
Converted equation
y = (-2/3)x + 4
General form with a common factor
2x - 4y + 8 = 0
Converted equation
y = (1/2)x + 2
Slope-intercept to standard
y = (2/3)x - 4
Converted equation
2x - 3y = 12
Decimal slope to standard
y = -0.75x + 1.5
Converted equation
3x + 4y = 6
Horizontal line
0x + 5y = 10
Converted equation
y = 2
Vertical line
3x + 0y = 9
Converted equation
x = 3
No x or y
0x + 0y = 4
Converted equation
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Frequently asked questions
How do you convert standard form to slope-intercept form?+
Start with Ax + By = C. Subtract Ax from both sides to get By = -Ax + C, then divide every term by B: y = (-A/B)x + C/B.
What is the slope of Ax + By = C?+
The slope is -A/B. For 2x + 3y = 12 the slope is -2/3. If B = 0 the line is vertical and the slope is undefined.
How do you convert y = mx + b to standard form?+
If m is a fraction, multiply every term by its denominator so the coefficients are integers. Then move the x-term to the left: y = (2/3)x - 4 becomes 3y = 2x - 12, then 2x - 3y = 12.
Should A be positive in standard form?+
Most textbooks write standard form with A positive and A, B, C as integers with no common factor. The calculator follows that convention, multiplying by -1 when needed.
What is the difference between standard form and general form?+
Standard form is Ax + By = C. General form is Ax + By + C = 0, with everything on one side. They contain the same information; the constant simply changes sign when it moves across.
What are the intercepts of Ax + By = C?+
Set y = 0 to get the x-intercept x = C/A, and set x = 0 to get the y-intercept y = C/B. This is why standard form is handy for graphing by intercepts.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026