Slope Intercept Form Calculator
Build a line's slope-intercept form (y = mx + b) and standard form from its slope and y-intercept, or from any two points — with x-intercept, slope classification, angle, and a step-by-step derivation.
Input
Output
| Metric | Value |
|---|---|
| No data yet | |
Guides
The Slope Intercept Form Calculator builds a line's slope-intercept form (y = mx + b) and standard form (Ax + By + C = 0) from whatever you already know — the slope and y-intercept directly, or any two points on the line — along with the x-intercept, a slope classification, the line's angle from the x-axis, and a step-by-step derivation.
It's built for students checking algebra homework, anyone graphing a line by hand, and for converting between the two most common line-equation forms without redoing the algebra manually.
How to use it
- Pick an Input Mode — "Slope & Y-Intercept" if you already have
mandb, or "Two Points" if you only have two coordinates on the line. - Fill in the fields for your chosen mode.
- Read the Result table for the slope, y-intercept, x-intercept, both equation forms, a slope classification, and the line's angle.
- Check Step-by-Step Solution for how the slope and y-intercept were derived.
Results update automatically as you type. For example, m = 2, b = -3 returns y = 2x - 3 and standard form -2x + y + 3 = 0.
Slope-intercept form vs. standard form
Slope-intercept form (y = mx + b) is the most direct way to read off a line's slope and where it crosses the y-axis. Standard form (Ax + By + C = 0) is the same line rewritten with everything on one side — useful for comparing two lines, checking for parallel/perpendicular slopes, or feeding into other algebra tools that expect that shape.
Building from two points
Given two points (x₁, y₁) and (x₂, y₂), the slope is m = (y₂ − y₁) / (x₂ − x₁) and the y-intercept follows from b = y₁ − m·x₁. If both points share the same x-coordinate, the line is vertical — its slope is undefined and it has no y = mx + b form at all, so the calculator reports x = <value> instead.
What is slope classification and angle?
The Slope Type row classifies the line as positive/negative/zero/undefined, and further as "steep" (|m| ≥ 1) or "shallow" (|m| < 1). The Angle from X-Axis is arctan(m) in degrees — how far the line tilts from horizontal, from 0° (flat) to 90° (vertical).
Privacy
This calculator runs entirely in your browser. Your numbers are never uploaded, logged, or stored — the computation happens locally on your device.
Use it from code
From 3 credits per callREST API
curl -X POST https://api.iotools.cloud/v1/tool/slope-intercept-form-calculator \
-H "Authorization: Bearer YOUR_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"inputMode": "slope-intercept",
"slope": "2",
"yIntercept": "-3"
}'Swap in your own key from your account. The tool's fields are the body — no wrapper.
Ask an AI agent
Use the IOTools `slope-intercept-form-calculator` tool (Slope Intercept Form Calculator) on this input:
YOUR_INPUT_HEREPaste this at any agent connected to the IOTools MCP server, then add your input.