Give this calculator two points, a slope plus one point, or a slope plus a y-intercept, and it builds the line's equation in slope-intercept form y = mx + b — along with the slope, y-intercept, x-intercept, and a second point on the line.
How the y = mx + b calculator works
Slope-intercept form is the friendliest way to write a line: y = mx + b says "start at height b on the y-axis, then rise m for every step right." Any non-vertical line can be written this way, and only two facts are ever needed to pin it down. This calculator accepts those two facts in whichever form you have them — two points, a slope and a point, or the slope and intercept directly — and hands back the finished equation plus everything it implies: both intercepts and a second point for graphing.
The formulas
m = (y₂ − y₁) ÷ (x₂ − x₁)
b = y − m·x (using any known point)
x-intercept: x = −b ÷ m
m is the slope, b is the y-intercept, and (x, y) is any point known to be on the line. Whichever mode you use, the calculator finds m first (or takes yours), then back-solves b, then reads everything else off the finished equation.
Worked example
Find the line through (1, 3) and (3, 7):
m = (7 − 3) ÷ (3 − 1) = 4 ÷ 2 = 2
b = 3 − 2×1 = 1, so the equation is y = 2x + 1.
Setting y = 0 gives the x-intercept: x = −1 ÷ 2 = −0.5. The line crosses the axes at (0, 1) and (−0.5, 0) and climbs two units for every one it moves right.
Reading an equation like a native
Once m and b are second nature, an equation stops being symbols and becomes a picture. y = 3 is a flat line at height 3 (m = 0, so the x term vanishes). y = x is the perfect 45° diagonal (m = 1, b = 0 — both invisible in the notation, which trips people up). y = −2x falls steeply through the origin. The one line the form can't express is a vertical one like x = 2: its slope would be division by zero, so it gets written as x = a instead — no y in sight. If you feed this calculator two points stacked vertically, it won't pretend otherwise; it tells you the slope is undefined and gives you the x = a equation instead.
Frequently asked questions
What do m and b stand for in y = mx + b?
m is the slope — how much y changes for every 1-unit increase in x — and b is the y-intercept, the value of y where the line crosses the y-axis (at x = 0). Together they pin down exactly one line: b tells you where to start, m tells you how steeply to tilt.
How do I find b if I know the slope and one point?
Plug the point into b = y − m·x. If the slope is 2 and the line passes through (1, 3), then b = 3 − 2×1 = 1, so the equation is y = 2x + 1. Any point on the line gives the same b, so use whichever one you have.
How do I find the equation of a line from two points?
Two steps: first find the slope m = (y₂ − y₁) ÷ (x₂ − x₁), then plug either point into b = y − m·x to get the y-intercept. This calculator does both and formats the finished equation for you.
What are the equations of horizontal and vertical lines?
A horizontal line has slope 0, so it's simply y = b — for example y = 3. A vertical line can't be written as y = mx + b at all: its slope is undefined because the run is zero, so it's written as x = a instead, like x = 2. If you enter two points with the same x, this calculator tells you exactly that.
How do I find the x-intercept from y = mx + b?
Set y to 0 and solve: 0 = mx + b gives x = −b ÷ m. For y = 2x + 1 that's x = −0.5, so the line crosses the x-axis at (−0.5, 0). Horizontal lines (m = 0) never cross the x-axis unless b is also 0 — in which case the line is the x-axis.