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Slope Formula (Gradient)
Coordinate Geometry • Grades 7, 8, 9, 10
Coordinate Geometry
Slope Formula (Gradient)
Find the steepness (rise over run) of any line passing through two points.
The Formula
m = (y₂ - y₁) / (x₂ - x₁)
Used for: Finding the steepness (rise over run) of a straight line passing through two points
mSlope / gradient of the line
ΔyVertical rise: (y₂ - y₁)
ΔxHorizontal run: (x₂ - x₁)
⚡Live Interactive Quick Solver
Instant CalculationSlope (m):1.33
Rise / Run: Δy = 4, Δx = 3 ➔ m = 4 / 3 = 1.33
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{\Delta y}{\Delta x}
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🎯 Key Concepts & Rules
Essential principles for calculating with this formula:
📈
m = (y₂ - y₁) / (x₂ - x₁)Vertical change (rise) divided by horizontal change (run).
↗️
Positive vs NegativePositive slopes rise to the right; negative slopes fall to the right.
⚠️
Zero vs UndefinedHorizontal lines have m = 0; vertical lines have undefined slope.
📝 Worked Examples & Step-by-Step Solutions
Example 1: Points (1, 3) and (5, 11)
Problem:
Find slope of line through (1, 3) and (5, 11).1
Rise (Δy)
y₂ - y₁ = 11 - 3 = 82
Run (Δx)
x₂ - x₁ = 5 - 1 = 43
Calculate
m = 8 / 4 = 2Answer: m = 2
💡 Pro Tips & Common Mistakes
Parallel Lines
Parallel lines have equal slopes: m₁ = m₂.
Perpendicular Lines
Perpendicular lines have negative reciprocal slopes: m₁ × m₂ = -1.
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