Slope Calculator
Calculate the slope between two points using the slope formula. Perfect for algebra, geometry, and finding the steepness of lines with step-by-step solutions and angle calculations.
Slope Calculator
Point 1 (x₁, y₁)
Point 2 (x₂, y₂)
Slope Result
Slope Type
Slope Formula
The slope formula calculates the steepness and direction of a line between two points. It's the ratio of the vertical change (rise) to the horizontal change (run).
Slope Formula
Understanding the formula behind slope calculations:
Example: Slope of (0,0) and (4,6) = (6-0) / (4-0) = 6/4 = 1.5
Types of Slopes
| Slope Type | Value | Description | Example |
|---|---|---|---|
| Positive | m > 0 | Line rises from left to right | m = 2 |
| Negative | m < 0 | Line falls from left to right | m = -1.5 |
| Zero | m = 0 | Horizontal line | m = 0 |
| Undefined | Division by 0 | Vertical line | x₁ = x₂ |
Common Slope Examples
| Point 1 | Point 2 | Slope | Type |
|---|---|---|---|
| (0, 0) | (4, 6) | 1.5 | Positive |
| (1, 5) | (3, 1) | -2 | Negative |
| (2, 3) | (7, 3) | 0 | Zero |
| (4, 1) | (4, 8) | Undefined | Vertical |
| (0, 0) | (1, 1) | 1 | 45° angle |
Applications
- Algebra: Analyze linear equations and graphing
- Engineering: Calculate gradients and inclines
- Architecture: Design ramps and roof slopes
- Physics: Analyze velocity and acceleration
- Economics: Study rate of change in data
Frequently Asked Questions
How do you find the slope between two points?
Use the slope formula: m = (y₂-y₁)/(x₂-x₁). Subtract the first y-coordinate from the second y-coordinate, then divide by the difference of the x-coordinates. This gives you the slope or steepness of the line.
What is the slope formula?
The slope formula is m = (y₂-y₁)/(x₂-x₁), where m represents the slope and (x₁,y₁) and (x₂,y₂) are two points on a line. It calculates the ratio of vertical change to horizontal change.
What does slope mean?
Slope measures the steepness and direction of a line. A positive slope means the line rises from left to right, negative slope means it falls, zero slope is horizontal, and undefined slope is vertical.
What is a negative slope?
A negative slope means the line decreases from left to right. As x increases, y decreases. For example, a slope of -2 means for every 1 unit right, the line goes down 2 units.
What is an undefined slope?
An undefined slope occurs when the denominator (x₂-x₁) equals zero, meaning both points have the same x-coordinate. This creates a vertical line, which has no defined slope.
How do you convert slope to angle?
Use the arctangent function: angle = arctan(slope). For example, if slope = 1, then angle = arctan(1) = 45°. Our calculator automatically converts slope to both degrees and radians.