Geometry Tool
Slope Calculator
Find the slope (m) of a line passing through two points.
Point 1
Point 2
Σ The Formula
m = (y₂ - y₁) / (x₂ - x₁)
Real World Examples
Positive Slope
(1,2) to (3,6) → m = (6-2)/(3-1) = 2
Negative Slope
(0,5) to (5,0) → m = (0-5)/(5-0) = -1
Horizontal Line
(2,3) to (5,3) → m = 0 (no rise)
Vertical Line
(4,1) to (4,5) → m = undefined (no run)
# About This Calculator
Slope (m) measures the steepness and direction of a line. Often described as "rise over run," it tells you how much the y-value changes for each unit change in x. A slope of 2 means the line rises 2 units for every 1 unit it runs horizontally.
Slope appears in countless real-world contexts: the grade of a road (6% grade = 0.06 slope), the pitch of a roof, the rate of change in economics (marginal cost), velocity in physics (distance over time), and trend analysis in data science.
Interpreting Slope
- Positive: Line goes UP from left to right.
- Negative: Line goes DOWN from left to right.
- Zero: Horizontal line (flat).
- Undefined: Vertical line (straight up).
How To Use
- Enter coordinates for **Point 1** ($x_1, y_1$).
- Enter coordinates for **Point 2** ($x_2, y_2$).
- Click **Calculate Slope**.
Frequently Asked Questions
What does a negative slope mean?+
A negative slope means the line goes downward from left to right. As x increases, y decreases. For example, a slope of -2 means for every 1 unit you move right, the line drops 2 units. Common in declining trends, downhill roads, or decreasing functions.
What's the difference between slope 0 and undefined slope?+
Slope 0 is a horizontal line (flat, like y = 3). Undefined slope is a vertical line (straight up/down, like x = 5). Zero slope has no rise; undefined slope has no run (division by zero).
How do I find the equation of a line from slope?+
Use point-slope form: y - y₁ = m(x - x₁), or slope-intercept form: y = mx + b. If you have slope m and a point (x₁, y₁), plug them into point-slope form. To get y-intercept b, solve for y when x = 0.
What does slope represent in real life?+
Slope represents rate of change: speed (distance/time), cost per item (price/quantity), grade of a hill (rise/run), efficiency (output/input), or any relationship where one variable changes relative to another. Steeper slope = faster change.
Are parallel lines related to slope?+
Yes! Parallel lines have identical slopes. Perpendicular lines have slopes that are negative reciprocals (if one is 2, the other is -1/2). This is crucial for geometry, coordinate proofs, and understanding line relationships.
Is Slope Calculator free to use?+
Yes, Slope Calculator on Matheric is completely free to use. We believe in accessible education and utility for everyone.