Slope Calculator
Calculate the slope from two points or one point and slope
Two Points Diagram
Enter Two Points
Point A
Point B
Point and Slope Diagram
Enter Point and Slope
Point
Slope & Distance
Slope Calculator Practice Quiz
Test your knowledge of slope calculations with these real-world scenarios. Select an answer for each question and submit to see if you're correct.
Formula
m = (y₂ - y₁) / (x₂ - x₁)
Step-by-Step Calculation
Result
Share Your Result
Graph
What is the Slope of a Line?
Slope tells us how steep a line is. It is calculated as the change in y divided by the change in x. A positive slope means the line is increasing, while a negative slope means it's decreasing.
Slope Definition
The slope of a line is a measure of its steepness and direction. It can be positive, negative, zero, or undefined.
Slope Formula Explained
m = rise/run = (y₂ - y₁) / (x₂ - x₁)
Examples of Different Slopes
Positive Slope
Line rises from left to right (e.g., m = 2)
Negative Slope
Line falls from left to right (e.g., m = -1.5)
Zero Slope
Horizontal line (e.g., m = 0)
Undefined Slope
Vertical line (e.g., x = constant)
Step-by-Step Slope Calculation Example
Let's calculate the slope of a line passing through points A(2, 3) and B(5, 9):
Step 1: Identify the coordinates
Point A: (x₁, y₁) = (2, 3)
Point B: (x₂, y₂) = (5, 9)
Step 2: Apply the slope formula
m = (y₂ - y₁) / (x₂ - x₁)
m = (9 - 3) / (5 - 2)
Step 3: Calculate the slope
m = 6 / 3 = 2
The slope of the line is 2, which means for every 1 unit of horizontal movement, the line rises 2 units vertically.
Slope Calculator Features
- Support for decimals and fractions
- Live graph plotting
- Visual rise/run triangle
- Line equation generator
- Step-by-step solutions
- Mobile-friendly interface
Graphical Representation of the Line
Our slope calculator provides a visual representation of the line with the two points marked. The slope triangle shows the rise and run, making it easier to understand the concept of slope.
The graph automatically adjusts to show the line in the best possible view, with the slope value clearly labeled.
Real-Life Applications of Slope
Road Gradients
Slope is used to determine the steepness of roads, ensuring safe driving conditions.
Construction and Design
Architects and engineers use slope calculations for ramps, roofs, and drainage systems.
Economics
Slope represents the rate of change in supply and demand curves.
Physics
In velocity-time graphs, slope represents acceleration.
Frequently Asked Questions (FAQ)
How do I calculate slope from two points?
To calculate the slope from two points, use the formula m = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.
What if the slope is undefined?
A slope is undefined when the line is vertical, which means x₂ - x₁ = 0. In this case, the line has an infinite slope.
What's the difference between rise/run and slope?
Rise/run is another way to express slope. Rise represents the vertical change (y₂ - y₁), while run represents the horizontal change (x₂ - x₁). The slope is the ratio of rise to run.
Can I calculate the equation of the line with one point and slope?
Yes, you can use the point-slope form of a line equation: y - y₁ = m(x - x₁), where (x₁, y₁) is the known point and m is the slope.
Disclaimer
This tool is for educational use only. We recommend verifying the results before applying them.
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