Quick answer
Slope-intercept form is y = mx + b, with b = y − m·x for a known point. Slope 2 through (1, 5) gives y = 2x + 3, a y-intercept of 3 and an x-intercept of −1.5.
Enter the slope and a point on the line. The calculator returns the equation and the intercepts.
Related tools: Standard Form to Slope-Intercept Form Calculator: Convert Ax + By = C to y = mx + b. 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 Slope-Intercept Form Calculator
- Enter slope (m).
- Enter point x.
- Enter point y.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Slope (m) | A number | — |
| Point x | A number | — |
| Point y | A number | — |
Formula and method
Formula
b = y − m·x; y = mx + b
IEEE-754 double precision; shown to at most 6 decimal places.
Solve for the intercept using the given point.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Slope (m) = 2; Point x = 1; Point y = 5.
| Result | Value |
|---|---|
| Equation | y = 2x + 3 |
| Y-intercept | 3 |
| X-intercept | -1.5 |
Example 2
Inputs: Slope (m) = 0; Point x = 4; Point y = 7.
| Result | Value |
|---|---|
| Equation | y = 7 |
| Y-intercept | 7 |
| X-intercept | none |
The first line is the headline result (equation). Below it the slope-Intercept Form Calculator lists y-intercept and x-intercept, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Intercepts
b = 5 − 2 × 1 = 3 is where the line crosses the y-axis. Setting y = 0: x = −b ÷ m = −1.5, where it crosses the x-axis.
Graphing
Start at (0, 3) and rise 2 for every 1 across. Vertical lines can't be written this way. Parallel lines share the slope; perpendicular lines have slopes that multiply to −1.
How the result changes with slope
Holding every other input at the first worked example, this table changes only slope. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Slope | Equation | Y-intercept | X-intercept |
|---|---|---|---|
| 1 | y = x + 4 | 4 | -4 |
| 2 | y = 2x + 3 | 3 | -1.5 |
| 4 | y = 4x + 1 | 1 | -0.25 |
| 8 | y = 8x − 3 | -3 | 0.375 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Slope (m): left empty shows "Enter slope (m)." beside that field and no result.
Choosing between the 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 |
|---|---|---|
| [Standard Form to Slope-Intercept Form Calculator](/math/standard-form-to-slope-intercept-form/) | a, b and c | Slope-intercept form |
| [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) |
| [LCM Calculator](/math/lcm-calculator/) | numbers | Least common multiple |
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
- Non-vertical lines
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 slope (m) to confirm this.
Frequently asked questions
What is the slope of y = −3x + 4?
y = −3x + 4 has slope −3, the coefficient of x.
What is the perpendicular slope to 2?
A perpendicular line has slope −1 ÷ 2 = −0.5.
How do I find the intercept?
Substitute a known point into y = mx + b and solve for b.
What does the Slope-Intercept Form Calculator calculate?
Line equation y = mx + b from a slope and a point. It returns Equation, Y-intercept and X-intercept.
What formula does the Slope-Intercept Form Calculator use?
b = y − m·x; y = mx + b. Solve for the intercept using the given point.
What do I need to enter in the slope-Intercept Form Calculator?
You enter Slope (m), Point x and Point y.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Non-vertical lines.
What is an example of a slope-Intercept Form result?
With slope (m) 2, point x 1 and point y 5, the equation is y = 2x + 3.
Related calculators
- Standard Form to Slope-Intercept Form Calculator — Convert Ax + By = C to y = mx + b.
- 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.
- LCM Calculator — Least common multiple of two or more numbers.
- Factor Calculator — List every factor of a positive whole number.
- 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.