Positive slope
A line rises from left to right when the y-value increases as x increases.
(1, 2) and (5, 10)
m = (10 - 2) / (5 - 1) = 2
Slope Calculator
Calculate the slope (m) between two points on a line with our easy-to-use slope calculator. The slope measures the steepness of a line and is a fundamental concept in mathematics.
Point 1
Point 2
What is Slope?
Slope is a measure of the steepness of a line. It tells you how much the y-value changes for each unit change in the x-value. Slope is commonly denoted by the letter m in the equation of a line y = mx + b, where b is the y-intercept.
Slope Formula
m = (y₂ - y₁) / (x₂ - x₁)
Where (x₁, y₁) and (x₂, y₂) are two distinct points on the line. The slope is calculated by finding the ratio of the 'rise' (the vertical change) to the 'run' (the horizontal change).
How to Calculate Slope
- Identify two points on the line, labeled as (x₁, y₁) and (x₂, y₂).
- Find the difference in y-coordinates: y₂ - y₁ (the rise).
- Find the difference in x-coordinates: x₂ - x₁ (the run).
- Divide the rise by the run to get the slope: m = (y₂ - y₁) / (x₂ - x₁).
Applications of Slope
Understanding slope has many practical applications:
- In engineering, slope is used to calculate gradients for roads, ramps, and roofs.
- In economics, slope can represent marginal costs, marginal revenue, or the rate of change in any economic function.
- In statistics, the slope of a regression line indicates the relationship between variables.
Slope Examples
Negative slope
A line falls from left to right when the y-value decreases as x increases.
(2, 8) and (6, 4)
m = (4 - 8) / (6 - 2) = -1
Undefined slope
Vertical lines have no defined slope because the run is zero.
(3, 1) and (3, 9)
Undefined because x₁ = x₂
Slope Calculator FAQ
What does a positive slope mean?
A positive slope means the line rises as you move from left to right. The y-value increases when the x-value increases.
What does a negative slope mean?
A negative slope means the line falls from left to right. The y-value decreases as the x-value increases.
Why is the slope undefined for a vertical line?
A vertical line has no horizontal change, so the run is zero. Division by zero is undefined, so the slope is undefined.
Where is slope used outside math class?
Slope appears in construction, map elevation, economics, physics, data analysis, and any situation where you need to measure rate of change.