Slope-Intercept Form Calculator
Enter two points below to instantly get the equation of the line in y = mx + b form.
Finding Slope-Intercept Form
m = (y₂ − y₁) / (x₂ − x₁), then b = y₁ − m·x₁.
Worked example
Points (1, 2) and (3, 8).
m = (8 − 2) / (3 − 1) = 6 / 2 = 3
b = 2 − 3(1) = −1
Equation: y = 3x − 1
A second example
Points (−1, 4) and (2, −5).
m = (−5 − 4) / (2 − (−1)) = −9 / 3 = −3
b = 4 − (−3)(−1) = 4 − 3 = 1
Equation: y = −3x + 1
Keep going
- Slope-intercept and point-slope are two ways to write the same line's equation; the point-slope calculator builds it from a single point and slope instead of the y-intercept. Point-Slope Form Calculator
- Slope-intercept form starts with the slope between two points; the slope calculator finds just that number on its own. Slope Calculator
Frequently Asked Questions
What is slope-intercept form?
Slope-intercept form writes a line's equation as y = mx + b, where m is the slope and b is the y-intercept (where the line crosses the y-axis).
How do you find the equation of a line from two points?
First find the slope: m = (y₂ − y₁) / (x₂ − x₁). Then plug one point and the slope into y = mx + b and solve for b.
What does the slope tell you?
The slope is how much y changes for every one-unit increase in x. A positive slope rises left to right; a negative slope falls; a slope of 0 is a flat horizontal line.
Can every line be written in slope-intercept form?
No — vertical lines (like x = 4) have an undefined slope, so they can't be written as y = mx + b. Every non-vertical line can be, including horizontal lines, which simply have m = 0.
What's a common mistake when solving for b?
A sign error when isolating b. Once you rearrange y = mx + b to b = y − mx, plug in one known point's x and y along with the slope you already found — dropping a negative sign here is the most frequent source of a wrong final equation.
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