Point-Slope Form Calculator
Build a line's equation from a point (x₁, y₁) and its slope m. Returns the point-slope form, slope-intercept form, and standard form, with a step-by-step derivation.
Input
x-coordinate of the known point.
y-coordinate of the known point.
Slope of the line.
Output
Guides
The Point-Slope Form Calculator builds a line's equation from a single point — (x₁, y₁) — and its slope, m. Enter the three values and it instantly returns the equation in three standard forms: point-slope, slope-intercept, and standard form, along with a step-by-step derivation showing how each one was reached.
It's built for algebra students, teachers preparing worked examples, and anyone who needs a line's equation without doing the substitution by hand.
How to use it
- Enter x₁ and y₁ — the coordinates of a point the line passes through.
- Enter m — the slope of the line.
- Read the three equation fields, or Step-by-Step Derivation for the full working.
Results update automatically as you type. For example, entering x₁ = 2, y₁ = 3, m = 4 returns y - 3 = 4(x - 2) in point-slope form, y = 4x - 5 in slope-intercept form, and 4x - y = 5 in standard form.
What is point-slope form?
Point-slope form is y − y₁ = m(x − x₁). It's the most direct way to write a line's equation when you know one point on the line and its slope, since both values plug straight in with no rearranging.
How is slope-intercept form derived?
Expanding and solving the point-slope equation for y gives y = mx + b, where the y-intercept b = y₁ − m·x₁. This is the form most useful for graphing, since m and b can be read directly off the equation.
How is standard form derived?
Standard form writes the equation as Ax + By = C, rearranging mx − y = −b so the x-coefficient stays non-negative. A horizontal line (m = 0) has no x-term, so it's reported simply as y = b rather than a degenerate "0x + y = b".
What if the line is vertical?
A vertical line has an undefined slope and can't be described by a single m value, so this calculator — like the point-slope formula itself — only handles lines with a defined slope. A vertical line through x = k is simply x = k, with no slope to enter.
For other coordinate-geometry basics, see the Midpoint Calculator to find the point halfway between two coordinates, or the Quadratic Formula Solver for solving curved (non-linear) equations.
Privacy
This calculator runs entirely in your browser. Your coordinates and slope 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/point-slope-form-calculator \
-H "Authorization: Bearer YOUR_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"x1": "2",
"y1": "3",
"slope": "4"
}'Swap in your own key from your account. The tool's fields are the body — no wrapper.
Ask an AI agent
Use the IOTools `point-slope-form-calculator` tool (Point-Slope Form Calculator) on this input:
YOUR_INPUT_HEREPaste this at any agent connected to the IOTools MCP server, then add your input.