X and Y Intercept Calculator
Find where a line ax + by + c = 0 crosses the x-axis and y-axis. Returns both intercept points, the slope, a plain-English line classification, and a step-by-step derivation.
Input
Coefficient of x.
Coefficient of y.
Constant term.
Output
More ways to use this tool
REST API
curl -X POST https://api.iotools.cloud/v1/tool/x-y-intercept-calculator \
-H "Authorization: Bearer YOUR_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"a": "2",
"b": "3",
"c": "-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 `x-y-intercept-calculator` tool (X and Y Intercept Calculator) 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/x-y-intercept-calculator/"
width="100%" height="520" frameborder="0" scrolling="no" loading="lazy"
title="X and Y Intercept Calculator — 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 |
|---|---|
| Need more credits? | View pricing |
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Guides
The X and Y Intercept Calculator finds where a line — written as ax + by + c = 0 — crosses the x-axis and y-axis. Enter the three coefficients and it returns both intercept points, the slope, a plain-English classification (horizontal, vertical, or oblique), and a step-by-step derivation.
It's built for algebra students, teachers preparing worked examples, and anyone who needs a line's intercepts without rearranging the equation by hand.
How to use it
- Enter a — the coefficient of x.
- Enter b — the coefficient of y.
- Enter c — the constant term.
- Read the X-Intercept and Y-Intercept fields, or Step-by-Step Derivation for the full working.
Results update automatically as you type. For example, entering a = 2, b = 3, c = -6 returns an x-intercept of (3, 0) and a y-intercept of (0, 2).
How are the intercepts found?
The x-intercept is the point where the line crosses y = 0, so setting y to 0 in ax + by + c = 0 and solving gives x = -c/a. The y-intercept works the same way in reverse: setting x to 0 gives y = -c/b. The slope follows directly from the same equation: m = -a/b.
What if a or b is 0?
- a = 0 — there's no x term, so the line is horizontal: it has a y-intercept but never crosses the x-axis (unless the line sits exactly on it).
- b = 0 — there's no y term, so the line is vertical: it has an x-intercept but never crosses the y-axis (unless the line sits exactly on it), and its slope is undefined.
- a and b both 0 — there's no line to solve for, so the calculator flags this as invalid input.
For solving a one-variable linear equation directly, see the Linear Equation Solver. To build a line's equation from a point and a slope instead, see the Point-Slope Form Calculator.
Privacy
This calculator runs entirely in your browser. Your coefficients are never uploaded, logged, or stored — the computation happens locally on your device.