What is Slope?
Slope measures the steepness or incline of a line. It describes how much the y-coordinate changes for a unit change in the x-coordinate. Often called "rise over run," slope is fundamental in algebra, geometry, physics, and engineering.
Slope Formula
Where (x₁, y₁) and (x₂, y₂) are two distinct points on the line.
How to Calculate Slope (Step by Step)
- Step 1: Identify the coordinates of your two points.
- Step 2: Subtract y₁ from y₂ to find the vertical change (rise).
- Step 3: Subtract x₁ from x₂ to find the horizontal change (run).
- Step 4: Divide the rise by the run. If the run (x₂ − x₁) is zero, the slope is undefined – the line is vertical.
Extra Information You Get
- Y-Intercept (b): The point where the line crosses the y-axis (x=0). Calculated as b = y₁ − m·x₁.
- Equation of the Line: Slope-intercept form y = mx + b.
- Angle of Inclination: The angle the line makes with the positive x‑axis, given by arctan(m).
- Grade (Percentage): Slope expressed as a percentage (rise/run × 100), often used in road gradients.
Example Calculation
For points (2, 3) and (5, 11):
Rise = 11 − 3 = 8
Run = 5 − 2 = 3
Slope m = 8/3 ≈ 2.6667
Angle = arctan(2.6667) ≈ 69.44°
Grade = 266.67%
Equation: y = 2.6667x − 2.3333
When is Slope Used?
Slope calculations appear everywhere: designing wheelchair ramps, determining roof pitch, analyzing trends in data, calculating velocity in physics, and even setting the difficulty of hiking trails. This calculator gives you instant, accurate results for any two points.
