Glossary
slope
The slope of a line is its steepness — the rise (vertical change) divided by the run (horizontal change), or the m in y = mx + b.
The slope of a line is a number that says how steep it is and which way it leans. It is the rise over the run: the vertical change between two points divided by the horizontal change between the same two points. Through (2, 5) and (6, 13), the rise is 13 − 5 = 8 and the run is 6 − 2 = 4, so the slope is 8 ÷ 4 = 2. In the equation y = mx + b, the slope is the coefficient m — the number multiplying x — and b is the y-intercept, the point where the line crosses the vertical axis. A positive slope climbs from left to right, a negative one falls, a zero slope is flat, and a vertical line has an undefined slope (the run is 0). The standard error is to subtract the coordinates in different orders on the top and the bottom, which flips the sign: (5 − 13) ÷ (6 − 2) = −2.
Taught in
Related terms
- quadratic formula — The quadratic formula solves any equation ax² + bx + c = 0: x = (−b ± √(b² − 4ac)) ÷ (2a).
- ratio — A ratio compares two quantities by division, written with a colon or as a fraction — 2 to 3 means two parts of one thing for every three of another.
Source: OpenStax Prealgebra, Elementary Algebra and College Algebra, first editions (CC BY 4.0); NIST SP 811 (units). Each definition restates the two Mathematics guides in this exam, which carry the per-source citations on their own pages. (OpenStax 1e and NIST SP 811 accessed 2026-10-07)