Slope-Intercept Form Calculator — y = mx + b
Convert any two points, a point and slope, or slope and y-intercept into the slope-intercept equation y = mx + b. Evaluate y at any x, find intercepts, and plot the line.
Input method
- 1
Slope m = (y₂ − y₁) ÷ (x₂ − x₁)
(9 − 3) ÷ (4 − 1) = 2 - 2
y-intercept b = y₁ − m × x₁
3 − 2 × 1 = 1b is where the line crosses the y-axis (x = 0).
How does this calculator work?
Given two points (x₁,y₁) and (x₂,y₂): slope m = (y₂−y₁)/(x₂−x₁), y-intercept b = y₁ − m·x₁, giving y = mx + b. Example: points (1,3) and (4,9) → m = 2, b = 1, equation y = 2x + 1. Evaluate y at any x by substituting: at x = 5, y = 11.
Formula
How this is calculated
The slope-intercept form y = mx + b is the most compact way to describe a non-vertical straight line in the Cartesian plane. The slope m tells you how many units y changes for each unit of increase in x: a positive m tilts the line up to the right, a negative m tilts it down, and m = 0 gives a horizontal line. The y-intercept b is simply the y-value where the line crosses the vertical axis (x = 0).
When you give two points (x₁, y₁) and (x₂, y₂), the calculator first computes m = (y₂ − y₁)/(x₂ − x₁), then solves for b = y₁ − m·x₁. If x₁ = x₂ the line is vertical and has no slope-intercept form (it is written as x = constant). From a point and a slope the same back-calculation finds b. Entering m and b directly skips both steps.
The angle of inclination θ = arctan(m) converts the slope to the angle the line makes with the positive x-axis, in degrees. The x-intercept (where the line crosses the x-axis, y = 0) is found by setting y = 0 and solving: x = −b/m (undefined when m = 0 because a horizontal line never crosses the x-axis unless b = 0).
Frequently asked questions
Slope-intercept y = mx + b is solved for y and immediately shows the slope and y-intercept. Standard form Ax + By = C (where A, B, C are integers) is often used in algebra textbooks and systems of equations. Both describe the same line; one is not more correct than the other.
A vertical line has an undefined slope and cannot be written in slope-intercept form. Its equation is simply x = a constant, meaning every point on the line shares the same x-coordinate.
It means the line crosses the y-axis below the origin. The value of b in y = mx + b is simply where the line is when x = 0 — it can be any real number, positive, negative, or zero.
Also known as
TG we-Calculate Editorial Team. (2026). Slope-Intercept Form Calculator — y = mx + b [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/slope-intercept-form-calculator
TG we-Calculate Editorial Team. "Slope-Intercept Form Calculator — y = mx + b." TG we-Calculate. 2026. https://we-calculate.com/calculator/slope-intercept-form-calculator.
TG we-Calculate Editorial Team, "Slope-Intercept Form Calculator — y = mx + b," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/slope-intercept-form-calculator
@misc{wecalculate_slope_intercept_form_calculator, title = {Slope-Intercept Form Calculator — y = mx + b}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/slope-intercept-form-calculator}}, year = {2026}, note = {TG we-Calculate} }
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