Quick answer
Standard form Ax + By = C converts to slope-intercept form as y = (−A ÷ B)x + C ÷ B. For 2x + y = 3, y = −2x + 3, with slope −2 and y-intercept 3.
Enter A, B and C. The calculator returns the slope-intercept form, slope and y-intercept.
Related tools: Slope-Intercept Form Calculator: Line equation y = mx + b from a slope and a point. Point-Slope Form Calculator: Point-slope and slope-intercept equations of a line. Slope Calculator: Slope, angle, distance and line equation through two points.
How to use the Standard Form to Slope-Intercept Form Calculator
- Enter a.
- Enter b.
- Enter c.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| A | A number | — |
| B | A number | — |
| C | A number | — |
Formula and method
Formula
y = (−A ÷ B)x + C ÷ B
IEEE-754 double precision; shown to at most 6 decimal places.
Solve Ax + By = C for y; B must not be 0.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: A = 2; B = 1; C = 3.
| Result | Value |
|---|---|
| Slope-intercept form | y = -2x + 3 |
| Slope | -2 |
| Y-intercept | 3 |
Example 2
Inputs: A = 1; B = 2; C = 4.
| Result | Value |
|---|---|
| Slope-intercept form | y = -0.5x + 2 |
| Slope | -0.5 |
| Y-intercept | 2 |
The first line is the headline result (slope-intercept form). Below it the standard Form to Slope-Intercept Form Calculator lists slope and y-intercept, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Solving for y
Subtract 2x from both sides: y = −2x + 3. For 3x + 4y = 12, y = −0.75x + 3: slope −3/4 and intercept 3.
Vertical lines
When B = 0 the equation is x = C ÷ A, a vertical line with no slope-intercept form. The standard form is handy for intercepts: set x = 0 or y = 0.
How the result changes with a
Holding every other input at the first worked example, this table changes only a. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| A | Slope-intercept form | Slope | Y-intercept |
|---|---|---|---|
| 1 | y = -x + 3 | -1 | 3 |
| 2 | y = -2x + 3 | -2 | 3 |
| 4 | y = -4x + 3 | -4 | 3 |
| 8 | y = -8x + 3 | -8 | 3 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- B: entering "0" shows "B must not be 0 (vertical line)." beside that field and no result.
Choosing between the Standard Form to Slope-Intercept Form Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Slope-Intercept Form Calculator](/math/slope-intercept-form/) | slope, point x and point y | Equation |
| [Point-Slope Form Calculator](/math/point-slope-form/) | slope, point x₁ and point y₁ | Point-slope form |
| [Slope Calculator](/math/slope-calculator/) | x₁, y₁ and x₂ | Slope |
| [Vertex Form Calculator](/math/vertex-form/) | a, b and c | Vertex (h, k) |
| [Standard Form Calculator](/math/standard-form-calculator/) | coefficient and exponent | Standard form |
Background: algebra
Many algebra calculators rest on the same ideas: write the problem in a standard form, identify the coefficients, apply the formula and check the answer by substituting it back. For a quadratic ax² + bx + c = 0 the roots are (−b ± √(b² − 4ac)) ÷ 2a, and the discriminant b² − 4ac decides the kind of roots: positive gives two real roots, zero gives one repeated root and negative gives two complex conjugate roots.
If a = 0 the equation is linear, not quadratic. A sign slip on the −b term shifts both roots by the same amount, so substitute your roots back to check.
Assumptions and limitations
- B = 0 is a vertical line
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for b to confirm this.
Frequently asked questions
What is the slope of 5x + 2y = 10?
Solve 5x + 2y = 10 for y: y = −2.5x + 5, so the slope is −2.5.
What is standard form?
Standard form writes a line as Ax + By = C with integer coefficients, e.g. 2x + y = 3.
Can B be zero?
Then the line is vertical.
What does the Standard Form to Slope-Intercept Form Calculator calculate?
Convert Ax + By = C to y = mx + b. It returns Slope-intercept form, Slope and Y-intercept.
What formula does the Standard Form to Slope-Intercept Form Calculator use?
y = (−A ÷ B)x + C ÷ B. Solve Ax + By = C for y; B must not be 0.
What do I need to enter in the standard Form to Slope-Intercept Form Calculator?
You enter A, B and C.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. B = 0 is a vertical line.
What is an example of a standard Form to Slope-Intercept Form result?
With a 2, b 1 and c 3, the slope-intercept form is y = -2x + 3.
Related calculators
- Slope-Intercept Form Calculator — Line equation y = mx + b from a slope and a point.
- Point-Slope Form Calculator — Point-slope and slope-intercept equations of a line.
- Slope Calculator — Slope, angle, distance and line equation through two points.
- Vertex Form Calculator — Convert y = ax² + bx + c to vertex form.
- Standard Form Calculator — Convert scientific notation to a standard decimal number.
- LCM Calculator — Least common multiple of two or more numbers.
- Row Echelon Form Calculator — Reduced row echelon form and rank of a matrix.
Sources
- OpenStax, Algebra and Trigonometry 2e (Rice University): exponents, radicals, logarithms and inverse trigonometric functions
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.