slope
Slope measures how steep a line is — the same idea as the grade of a road or a wheelchair ramp. A big slope is a steep climb; a small slope is a gentle one; a flat road has slope zero.
Numerically, the slope of a line (usually written m) is the ratio of vertical change to horizontal change between any two points on it: m = (y₂ − y₁) / (x₂ − x₁). A positive slope rises left to right, a negative slope falls, and a horizontal line has slope 0. Because a line is perfectly straight, you get the same value of m no matter which two points you pick.
A vertical line is the one exception: its horizontal change is 0, so the ratio would divide by zero. Division by zero is undefined, so we say a vertical line has no slope (undefined slope) — not slope zero.
Through (1, 2) and (4, 8): m = (8 − 2) / (4 − 1) = 6/3 = 2. The line rises 2 units of height per 1 unit across.
Slope = change in y over change in x.
Horizontal line: slope 0. Vertical line: slope undefined. These are different and worth memorizing separately.