Slope Calculator – Guide & Formulas
Calculate the slope (m), angle, y-intercept, and distance between two coordinates. Learn step-by-step slope formulas.
Determine the slope of a line passing through two coordinate points (x₁, y₁) and (x₂, y₂). Solves for steepness, angle of inclination, and y-intercept instantly.
Key Takeaway
Use the free Slope Calculator to calculate the slope (m), angle, y-intercept, and distance between two coordinates. learn step-by-step slope formulas. Get instant results with step-by-step explanations.
How to Use the Slope Calculator
- Enter the coordinates for the first point (x₁, y₁).
- Enter the coordinates for the second point (x₂, y₂).
- Analyze the resulting slope m, its rise-over-run fraction, inclination angle, and y-intercept.
The Formula
Variable Definitions
- m: Slope of the line (steepness)
- (x1, y1): Coordinates of the first point
- (x2, y2): Coordinates of the second point
Determining the Slope of a Ramp
A ramp starts at point (2, 3) and ends at point (10, 7). Find its slope and steepness ratio.
- Step 1: Identify coordinates: (x₁, y₁) = (2, 3) and (x₂, y₂) = (10, 7).
- Step 2: Apply the slope formula: m = (7 - 3) / (10 - 2).
- Step 3: Simplify the rise and run: m = 4 / 8 = 0.5 (or 1/2).
- Step 4: The ramp slope is 0.5 with an inclination angle of approximately 26.57°.
Frequently Asked Questions
What does a zero slope mean?
A slope of zero represents a perfectly horizontal flat line, where there is no vertical change (rise = 0).
What is an undefined slope?
An undefined slope occurs on a perfectly vertical line, where the change in x is zero (run = 0), leading to a division by zero.
How do you find slope from an equation?
In slope-intercept form (y = mx + b), the coefficient of x (which is m) is the slope.