# Point Slope Form Calculator

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

> The point slope form calculator writes the line through a point with a given slope as y − y₁ = m(x − x₁), converts it to slope-intercept and standard form, and evaluates y at any x.

## Inputs

- x₁
- y₁
- Slope m
- Find y at x =

## Results

- Point-slope form
- Slope-intercept form
- Standard form
- x-intercept
- y at the chosen x

## Formula

```
y − y₁ = m(x − x₁)
```

## Explanation

Point-slope form is the quickest way to write a line when you know one point and the slope – for example a cost that starts at $40 for 2 hours and rises $15 per hour.

### How to use the Point Slope Form Calculator

- **x₁**
- **y₁**
- **Slope m**
- **Find y at x =**

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

### How it works

The point and slope are substituted directly. Expanding gives slope-intercept form; clearing fractions gives integer standard form.

## Worked example

Inputs — x₁: 2; y₁: 3; Slope m: 0.5; Find y at x =: 4.

Results — **Point-slope form = y − 3 = (1/2)(x − 2)**; Slope-intercept form = y = (1/2)x + 2; Standard form = x − 2y = −4; x-intercept = −4; y at the chosen x = 4.

## Key terms

- **Point-slope form**: y − y₁ = m(x − x₁).

## FAQ

**How do I write a line with slope 3 through (1, 4)?**
y − 4 = 3(x − 1), or y = 3x + 1.

**How do I convert to slope-intercept form?**
Distribute m and add y₁ to both sides.

**Can point-slope form describe a vertical line?**
No – vertical lines have no slope; use x = x₁.

**Is point-slope form unique?**
No – any point on the line gives a valid version.


## Sources

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