➕ Algebra 1 · Linear Functions
Parallel and Perpendicular Lines cheat sheet
Everything you need on one page. Print it, or switch on test-yourself mode to blur the answers and check your memory.
Parallel
- Same slope, different y-intercepts
- Two different vertical lines are parallel
- Same slope and same y-intercept: the same line
Perpendicular
- Slopes are negative reciprocals: product −1
- Flip the fraction, then change the sign
- Horizontal and vertical lines are perpendicular
Test two lines
- Check for vertical lines (x = a) first
- Solve both for y (divide every term)
- Compare slopes: same, product −1, or neither
Write a new line (SLIP)
- S: Slope of the given line
- L: Look (same for parallel, flip and change sign for perpendicular)
- I: Insert the point into y = mx + b
- P: Pull out b, write the equation
Example
- Through (8, 3), perpendicular to y = (4/5)x − 6
- New slope: −5/4
- 3 = −(5/4)(8) + b, so b = 13
- y = −(5/4)x + 13
Formulas
- Parallel: m1 = m2 and b1 ≠ b2 (different lines)
- Perpendicular: m1 × m2 = −1, so m2 = −1/m1 (when m1 ≠ 0)
- Slope from standard form: Ax + By = C with B ≠ 0 has slope −A/B and y-intercept C/B
- Special pair: y = b (horizontal) and x = a (vertical) are perpendicular
Parallel and Perpendicular Lines cheat sheet from HighSchoolQ.com, for personal study use.