Slope Calculator
Calculate the slope of a line through two given points, or find the equation of a line given one point and the slope. Also calculates distance, angle, and other line properties.
Slope Calculation Results
| Slope (m) | 1 |
|---|---|
| Angle (θ) | 45° |
| Distance | 2.828 |
| Slope Percentage | 100% |
| Equation | y = x + 1 |
About Slope Calculator
The slope of a line is a measure of its steepness and direction. It's calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. Slope is fundamental in algebra, geometry, calculus, and many applied sciences.
How Slope is Calculated
Given two points (x₁, y₁) and (x₂, y₂) on a line, the slope m is calculated as:
m = (y₂ - y₁) / (x₂ - x₁)
Understanding Slope Values
Different slope values indicate different line characteristics:
- Positive slope: Line rises from left to right
- Negative slope: Line falls from left to right
- Zero slope: Horizontal line (no vertical change)
- Undefined slope: Vertical line (no horizontal change)
Slope and Angle Relationship
The angle θ that a line makes with the positive x-axis is related to the slope by:
θ = arctan(m)
Where m is the slope and θ is measured in degrees or radians.
Distance Between Two Points
The distance d between two points (x₁, y₁) and (x₂, y₂) is calculated using the distance formula:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Line Equations
There are several forms of line equations:
- Slope-intercept form: y = mx + b (m is slope, b is y-intercept)
- Point-slope form: y - y₁ = m(x - x₁)
- Standard form: Ax + By = C