Meet the star of this chapter: slope, written $m$. It answers one friendly question — for every step you walk ACROSS, how much does the path climb? Read aloud: slope equals rise over run: $m = \dfrac{\text{rise}}{\text{run}}$. A ramp that rises 1 m over a 4 m run has a slope of one quarter. That's the whole idea. Everything else in this chapter is the same idea wearing fancier clothes.

And the sign comes free, before any arithmetic: walking left to right, a path that climbs has a positive slope, one that drops is negative, and a flat boardwalk sits at exactly zero. A perfectly vertical wall? Its run is zero, the division goes on strike, and everyone — mathematicians included — calls that slope undefined. Read the direction first; the number will follow politely.