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.
Formula
y − y₁ = m(x − x₁)
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).
Frequently asked questions
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.