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Calculate slope from two points, find the equation in slope-intercept form (y=mx+b), and get parallel and perpendicular slopes. Step-by-step working shown.
Slope is a measure of the steepness and direction of a line, calculated as the ratio of vertical change (rise) to horizontal change (run) between two points: m = Δy/Δx.
Slope (m)
2
Y-Intercept (b)
0
Equation
y = 2x + 0
Distance
6.7082039
Perpendicular Slope
-0.5
Angle
63.434949°
Steps
Rise (Δy) = 8 − 2 = 6
Run (Δx) = 4 − 1 = 3
Slope = 6 / 3 = 2
Formula
m = (y₂ − y₁) / (x₂ − x₁)m = Slope of the line
(x₁, y₁) = First point on the line
(x₂, y₂) = Second point on the line
Worked Example
Slope from (1, 2) to (4, 8)
Did you know? The letter 'm' for slope likely comes from the French word 'monter' (to climb), though this etymology is debated. René Descartes, who invented coordinate geometry in 1637, did not use a specific letter for slope (source: Mathematical Association of America).
Sources
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