Calculate slope, y-intercept, and distance between two points on a coordinate plane — instantly.
The Slope Calculator finds the slope (m), y-intercept (b), and distance between any two points (x₁, y₁) and (x₂, y₂) on a coordinate plane. It gives you the complete equation of the line in slope-intercept form: y = mx + b.
What is Slope?
Slope measures the steepness and direction of a line. It is calculated as "rise over run" — how much y changes for every unit change in x. A positive slope goes up from left to right. A negative slope goes down. A slope of 0 is horizontal. An undefined slope (vertical line) occurs when x₁ = x₂.
Real-World Applications
- Engineering: Road grades (a 5% slope means 5m rise per 100m horizontal distance)
- Architecture: Roof pitch and ramp design
- Physics: Velocity as slope of distance-time graph; acceleration as slope of velocity-time graph
- Economics: Marginal cost, supply/demand curves
- Data analysis: Trend lines in scatter plots
Coordinate Geometry in Exams
Slope, distance formula, and line equations are core topics in Class 10-12 CBSE/ICSE mathematics and feature prominently in JEE, NEET (mathematics section), and all competitive aptitude exams.
1. Enter two points: (x₁, y₁) and (x₂, y₂) — the coordinates of any two points on the line.
2. View Results: Get slope (m), y-intercept (b) for the equation y = mx + b, and the straight-line distance between the two points.
Slope: m = (y₂ − y₁) / (x₂ − x₁)
Y-intercept: b = y₁ − m × x₁
(The point where the line crosses the y-axis)
Distance: d = √((x₂−x₁)² + (y₂−y₁)²)
(Pythagorean theorem applied to coordinates)
Line equation: y = mx + b
Example 1: Points (1, 2) and (4, 8) → m = (8−2)/(4−1) = 6/3 = 2. b = 2 − 2×1 = 0. Line: y = 2x. Distance = √(9+36) = √45 ≈ 6.708
Example 2: Points (0, 3) and (6, 0) → m = (0−3)/(6−0) = −0.5. b = 3. Line: y = −0.5x + 3. This is the standard form x/6 + y/3 = 1.