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Slope Intercept Form Calculator
Last updated: June 19, 2026
A slope intercept form calculator is an algebraic tool that determines the equation of a line in the standard form y equals mx plus b, where m represents the slope and b represents the y-intercept. The calculator computes the equation from various inputs, including two coordinate points, one point and the slope, or by converting a general linear equation. It outputs the slope, y-intercept, x-intercept, and displays the step-by-step mathematical work. Math students use this tool to verify coordinate geometry homework and graph lines.
Pick a starting point (two points, slope-plus-point, or standard form). Enter the values; the calculator returns y = mx + b along with the slope, y-intercept, and a worked step.
Quick Answer
Find the slope-intercept form equation of a line. Enter coordinates or an equation to calculate the slope (m) and y-intercept (b).
From
For just the slope between two points, use the slope calculator. To build y − y₁ = m(x − x₁), use the point-slope form calculator.
Equation
y = 3x - 1
m = 3; b = -1
Slope-intercept form makes the y-intercept visible at a glance: it is the constant term. The slope is the coefficient of x. A vertical line cannot be written in this form because its slope is undefined.
Examples
Two points (1,2), (3,8)
m = 3, b = −1, y = 3x − 1
Slope 3, point (1,4)
b = 1, y = 3x + 1
Standard 2x + 3y = 12
m = −2/3, b = 4, y = −0.667x + 4
Two points (0,5), (2,5)
Horizontal line y = 5
How it works
All three input modes lead to the same equation y = mx + b. Once you have the slope (or it is given), find b by plugging a known point into the equation and solving.
Slope · m = (y₂ − y₁) / (x₂ − x₁)
Intercept · b = y − m·x
From standard form · y = (−A/B)·x + (C/B)
Related calculators
- Slope calculator when you only need the slope between two points.
- Point slope form calculator to write the same line as y − y₁ = m(x − x₁).
- y = mx + b Calculator to calculate and graph the slope-intercept equation.
- Point-Slope Formula for step-by-step point-slope math.
- Linear regression calculator for the best-fit line through a dataset (also returns m and b).
- System of equations calculator for finding the intersection of two lines.
- All education calculators.
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Frequently asked questions
y = mx + b. m is the slope (rise over run), b is the y-intercept (the y value where the line crosses the y-axis). This form is the easiest to graph by hand.
First compute the slope m = (y₂ − y₁) / (x₂ − x₁). Then plug one of the points into y = mx + b and solve for b: b = y − m·x. The calculator does both steps.
Solve for y: subtract Ax from both sides to get By = −Ax + C, then divide by B: y = (−A/B)·x + (C/B). The slope is −A/B and the y-intercept is C/B. Requires B ≠ 0.
A vertical line has undefined slope and cannot be written as y = mx + b. The calculator flags this case and suggests writing the line as x = constant instead.
The slope calculator returns just the slope between two points. This page builds the full equation y = mx + b including the y-intercept. Use the slope calculator when you only need m.
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