Standard Form to Slope Intercept Converter
Convert a line from standard form (Ax + By = C) into slope-intercept form (y = mx + b), with the slope and y-intercept broken out — or a clear note when the line is vertical and has no slope-intercept form.
Input
Coefficient of x in Ax + By = C.
Coefficient of y. Zero means a vertical line, which has no slope-intercept form.
Constant on the right-hand side.
Output
More ways to use this tool
REST API
curl -X POST https://api.iotools.cloud/v1/tool/standard-form-to-slope-intercept-converter \
-H "Authorization: Bearer YOUR_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"coeffA": "2",
"coeffB": "3",
"coeffC": "6"
}'Swap in your own key from your account. The tool's fields are the body — no wrapper.
Ask an AI agent
Use the IOTools `standard-form-to-slope-intercept-converter` tool (Standard Form to Slope Intercept Converter) on this input:
YOUR_INPUT_HEREPaste this at any agent connected to the IOTools MCP server, then add your input.
Embed widget
<iframe
src="https://iotools.cloud/embed/standard-form-to-slope-intercept-converter/"
width="100%" height="520" frameborder="0" scrolling="no" loading="lazy"
title="Standard Form to Slope Intercept Converter — iotools.cloud"
sandbox="allow-scripts allow-forms allow-same-origin allow-downloads allow-popups allow-popups-to-escape-sandbox"
allow="clipboard-write"
style="width:100%;border:1px solid #e5e7eb;border-radius:12px;overflow:hidden"></iframe>
<script src="https://iotools.cloud/embed.js" async></script>Drop this into your own page — free, no key required, just a link back.
| Cost per API/MCP call | From 5 credits |
|---|
Also available with
Guides
Given a line as Ax + By = C — standard form, the shape a textbook problem or another tool's output most often hands you — this converter solves it for y, returning the slope-intercept form (y = mx + b) along with the slope and y-intercept broken out on their own.
How to use it
- Enter A, B, and C from your equation
Ax + By = C. - Read off the standard form (echoed back so you can confirm it parsed correctly), the slope, the y-intercept, and the slope-intercept form.
Results update automatically as you type. For example, 2x + 3y = 6 returns slope -0.666667, y-intercept 2, and y = -0.666667x + 2.
The method
Solving Ax + By = C for y:
By = -Ax + C
y = (-A/B)x + (C/B)so m = -A/B and b = C/B.
When B = 0
If B is zero, the equation reduces to Ax = C — a vertical line, x = C/A. A vertical line has an undefined slope and no y = mx + b form at all, so the calculator reports that directly instead of dividing by zero.
FAQ
What if A is zero?
A = 0 gives By = C, a horizontal line with slope 0 — the slope-intercept form is just y = C/B, a constant.
Can A, B, and C be decimals?
Yes — coefficients aren't limited to whole numbers.
Related tools
To go the other direction — build both standard form and slope-intercept form starting from a slope and y-intercept, or from two points — see the Slope Intercept Form Calculator.
Privacy
This calculator runs entirely in your browser. Your numbers are never uploaded, logged, or stored — the computation happens locally on your device.