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Slope Calculator
Find the slope, midpoint, distance, and standard linear equations of a line passing through two coordinate points.
Input Coordinates
Results
| Slope (m) | — |
|---|---|
| Distance (d) | — |
| Midpoint | — |
| Angle of Inclination (θ) | — |
| Slope-Intercept Form | — |
| Point-Slope Form | — |
| Standard Form | — |
Understanding Slope
The **Slope** of a line is a measure of its steepness and direction. Often described as "rise over run", it represents the vertical change divided by the horizontal change between two distinct points on the line.
The Slope Formula
For any two points $(x_1, y_1)$ and $(x_2, y_2)$ on a cartesian plane, the slope $m$ is: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ If $x_1 = x_2$, the denominator is zero, meaning the slope is **undefined** (a vertical line).
Linear Equation Forms
Once the slope $m$ is known, you can represent the line mathematically:
- **Slope-Intercept Form:** $y = mx + b$, where $b$ is the y-intercept.
- **Point-Slope Form:** $y - y_1 = m(x - x_1)$.
- **Standard Form:** $Ax + By = C$, where $A, B,$ and $C$ are integers.