Math & Statistics · 斜率与截距（Slope & Intercept） · Updated 2026-10-25
What Is Slope & Intercept?
Definition
In y=kx+b, the slope k=(y₂−y₁)/(x₂−x₁) says how y moves per unit of x, and b is the y-intercept (value at x=0). Two points fix the line: compute k, then substitute to get b. Linear regression is exactly fitting k and b: bill = price k × usage + fixed fee b. Vertical lines have undefined slope (zero denominator); horizontal lines have k=0. Negative slope encodes inverse relations — "each extra 10k of income cuts 0.4 commute minutes" is the same math.
Formula
k = (y₂ − y₁)/(x₂ − x₁); y = kx + b
Worked Example
A taxi charging 8 base + 2.5/km: y=2.5x+8 (k=2.5 per km, b=8 base); 12 km costs 38 yuan.
Common Misconception
"A big slope means big values" — slope is a rate, not a level; k=1000 yields y=1 at x=0.001. And b is not necessarily positive — intercepts can be negative (starting in debt) or zero (pure proportional pricing); b is simply the reading at x=0.
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