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Slope (gradient) measures the steepness of a line: rise over run = Δy/Δx = (y₂−y₁)/(x₂−x₁). Positive slope = rising left to right; negative = falling; zero = horizontal; undefined = vertical. Used in algebra, physics, road engineering, and data analysis.
Guida passo passo
- 1m = (y₂ − y₁) / (x₂ − x₁)
- 2Slope-intercept form: y = mx + b (m=slope, b=y-intercept)
- 3Parallel lines have equal slopes
- 4Perpendicular lines: slopes are negative reciprocals (m₁ × m₂ = −1)
Esempi risolti
Ingresso
Points (1, 2) and (4, 8)
Risultato
Slope = (8−2)/(4−1) = 6/3 = 2
For every 1 right, go 2 up
Ingresso
Slope of 1/4 in road engineering
Risultato
25% grade
1 ft rise per 4 ft run
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