# Slope & Line Equation Calculator — Slope-Intercept, Point-Slope & Standard

> Find the slope and equation of a line from two points: slope-intercept (y = mx + b), point-slope and standard forms, intercepts, midpoint, distance and angle, with a graph.

- **Category:** Math
- **Interactive calculator:** https://youcalc.com/en/math/slope-line-equation/
- **Price:** Free, no sign-up required

## Overview

This calculator finds every property of the line through two points you enter: slope, y-intercept, x-intercept, slope-intercept form (y = mx + b), point-slope form, standard form (Ax + By = C), the midpoint, the distance between the points, and the angle of inclination. An interactive graph shows the line and both points at a glance.

## How to read your result

Enter the coordinates of your two points and the results update instantly. The headline result card shows the slope-intercept equation. Below it, a detail panel lists the point-slope form, standard form, midpoint, and distance. A small graph renders the line and highlights the two input points. The slope and angle of inclination also appear in the stat strip at the top of the page.

## Method

The slope is m = (y₂ − y₁) / (x₂ − x₁). The y-intercept follows from b = y₁ − m·x₁ and the x-intercept from −b/m. Standard form coefficients are derived from (y₂ − y₁)x − (x₂ − x₁)y = (y₂ − y₁)x₁ − (x₂ − x₁)y₁, then reduced by the GCD of the integer coefficients and normalized so A ≥ 0. The angle of inclination is arctan(m) in degrees, shifted to [0°, 180°) for negative slopes. Formulas follow Wolfram MathWorld: Slope-Intercept Form and Slope.

## Example

- **Setup:** Enter point 1 as (1, 3) and point 2 as (4, 9).
- **Result:** The calculator returns slope 2, y-intercept 1, x-intercept −0.5, equation y = 2x + 1, standard form 2x − y = −1, midpoint (2.5, 6), distance approximately 6.708, and angle of inclination about 63.43°.

## Frequently asked questions

### What does the slope tell me?

The slope (m) measures how steeply the line rises or falls. A slope of 2 means the line goes up 2 units for every 1 unit it moves to the right. A negative slope means the line falls from left to right, and a slope of zero means the line is horizontal. A vertical line has no defined slope.

### What is the difference between the three equation forms?

Slope-intercept form (y = mx + b) is the most convenient for reading off the slope and y-intercept directly. Point-slope form (y − y₁ = m(x − x₁)) is useful when you know one point and the slope. Standard form (Ax + By = C) keeps all variables on one side and is common in systems of equations. All three represent the same line.

### How are the midpoint and distance calculated?

The midpoint is the average of the two x-coordinates and the average of the two y-coordinates: ((x₁ + x₂)/2, (y₁ + y₂)/2). The distance is the length of the straight segment between the two points, found with the Pythagorean theorem: √((x₂ − x₁)² + (y₂ − y₁)²).

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- [Quadratic Equation Solver](https://youcalc.com/en/math/quadratic-equation/)
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- [Triangle Solver](https://youcalc.com/en/math/triangle-solver/)

## Sources

- https://mathworld.wolfram.com/Slope-InterceptForm.html
- https://mathworld.wolfram.com/Slope.html

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Interactive version: https://youcalc.com/en/math/slope-line-equation/ · From YouCalc — https://youcalc.com