➕ Algebra 1 · Linear Functions
Standard Form of a Line 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
- Ax + By = C (A, B not both 0)
- A goes with x, B goes with y, signs included
- The graph is a straight line
The usual convention
- WAT: Without fractions, A not negative, Trimmed (no common factor)
- A convention, not a law of math
Intercepts: cover a term
- Cover y, find x: x = C/A, point (C/A, 0)
- Cover x, find y: y = C/B, point (0, C/B)
- If C = 0, both intercepts are 0
Convert
- To y = mx + b: m = −A/B and b = C/B (if B ≠ 0)
- To standard form: clear fractions, move the x term, make A not negative
Special lines
- A = 0: horizontal, slope 0
- B = 0: vertical, slope undefined
Example
- 4x + 3y = 24
- Cover 3y: x = 6. Cover 4x: y = 8.
- Points (6, 0) and (0, 8), check (3, 4)
Formulas
- Standard form: Ax + By = C, with A and B not both 0
- x-intercept: x = C/A (if A ≠ 0), so the line crosses at (C/A, 0)
- y-intercept: y = C/B (if B ≠ 0), so the line crosses at (0, C/B)
- Slope: m = −A/B (if B ≠ 0)
- Horizontal line: A = 0: y = C/B, slope 0
- Vertical line: B = 0: x = C/A, slope undefined
Standard Form of a Line cheat sheet from HighSchoolQ.com, for personal study use.