➕ Algebra 1 · Linear Functions
Point-Slope Form cheat sheet
Everything you need on one page. Print it, or switch on test-yourself mode to blur the answers and check your memory.
The form
- y − y1 = m(x − x1)
- m = slope, (x1, y1) = one known point on the line
- x and y stay as letters
Read it (flip the sign)
- In y − y1 = m(x − x1), flip the sign you see:
- y − 8 means y1 = 8. y + 8 means y1 = −8.
- x − 3 means x1 = 3. x + 3 means x1 = −3.
- The slope keeps the sign in front of it.
- A lone x or y means that coordinate is 0.
Write it
- Point and slope: put them in, then simplify double negatives
- Two points: find m first (Slope, Pick, Plug)
- Vertical line: x = a, no point-slope form
Convert to $y = mx + b$
- Distribute m to both terms
- Move the number next to y to the right side
- b = y1 − m × x1
Example
- Points (−4, 3) and (2, −1)
- m = −4/6 = −2/3
- y + 1 = −(2/3)(x − 2)
- y = −(2/3)x + 1/3
Formulas
- Point-slope form: y − y1 = m(x − x1)
- Slope from two points: m = (y2 − y1) ÷ (x2 − x1), assuming x2 ≠ x1
- To slope-intercept form: y = mx + b, where b = y1 − m × x1
- Horizontal line (m = 0): y − y1 = 0, which is y = y1
- Vertical line: x = a (slope undefined, no point-slope form)
Point-Slope Form cheat sheet from HighSchoolQ.com, for personal study use.