Point-Slope Form: Write a Line From a Point and Slope
How to use point-slope form to write a line, with two worked examples.
The formula
- y − y₁ = m(x − x₁)
- m = (y₂ − y₁) / (x₂ − x₁)
Use it when you know a point (x₁, y₁) and the slope m.
Example 1
Write the line through (2, 5) with slope 3.
- y − 5 = 3(x − 2)
- y − 5 = 3x − 6
y = 3x − 1
Example 2
Write the line through (1, 2) and (3, 8).
- m = (8 − 2)/(3 − 1) = 3
- y − 2 = 3(x − 1)
y = 3x − 1
Common mistake
y − 5 = 3(x + 2) for the point (2, 5)
The signs flip: a point (2, 5) gives (x − 2) and (y − 5).
A point like (−2, 5) gives (x + 2).
Want more Algebra 1 practice?
The free Algebra 1 study guide has quizzes, flashcards and practice exams. 100% free, no sign-up needed.
Open the Algebra 1 guide