# Slope Intercept Form Calculator

URL: https://speedycalculator.com/calculators/math/slope-intercept-form/
Last updated: 2026-10-30

> The slope intercept form calculator finds y = mx + b for the line through two points, with exact fractions, the x-intercept and the standard form.

## Inputs

- x₁
- y₁
- x₂
- y₂

## Results

- y = mx + b
- Slope m
- y-intercept b
- Standard form
- Point-slope form

## Formula

```
m = (y₂ − y₁)/(x₂ − x₁),  b = y₁ − m·x₁
```

## Explanation

Slope-intercept form shows the two most useful facts about a line at a glance: its steepness m and where it crosses the y-axis, b. It is the form used for graphing and for linear models such as cost = fixed fee + rate × quantity.

### How to use the Slope Intercept Form Calculator

- **x₁**
- **y₁**
- **x₂**
- **y₂**

Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.

### How it works

The slope comes from the two points and the intercept from substituting one point. Fractions are kept exact where possible.

## Worked example

Inputs — x₁: 1; y₁: 2; x₂: 4; y₂: 3.

Results — **y = mx + b = y = (1/3)x + 5/3**; Slope m = 1/3 ≈ 0.33333333; y-intercept b = 5/3; Standard form = x − 3y = −5; Point-slope form = y − 2 = (1/3)(x − 1).

## Key terms

- **y-intercept**: Where a line crosses the y-axis.

## FAQ

**How do I find slope-intercept form from two points?**
Compute m, then b = y₁ − m·x₁.

**What is the x-intercept?**
−b/m, where y = 0.

**How do I graph y = mx + b?**
Plot (0, b) and move 1 right and m up.

**Can every line be written this way?**
All except vertical lines.


## Sources

- [OpenStax – College Algebra 2e](https://openstax.org/details/books/college-algebra-2e)
- [OpenStax – Precalculus 2e](https://openstax.org/details/books/precalculus-2e)