Slope Calculator
Enter the coordinates of two points (x1, y1) and (x2, y2) to calculate the slope of the line connecting them.
Result:
Understanding the Slope of a Line
The slope of a line is a fundamental concept in mathematics that describes its steepness and direction. It's a measure of how much the line rises or falls vertically for every unit it moves horizontally. Understanding slope is crucial in various fields, including geometry, physics, engineering, and economics, as it represents a rate of change.
What is Slope?
In simple terms, slope tells you how steep a line is. A larger absolute value of slope indicates a steeper line. The sign of the slope tells you the direction:
- Positive Slope: The line goes upwards from left to right. This means as 'x' increases, 'y' also increases.
- Negative Slope: The line goes downwards from left to right. This means as 'x' increases, 'y' decreases.
- Zero Slope: The line is perfectly horizontal. This means 'y' does not change as 'x' changes.
- Undefined Slope: The line is perfectly vertical. This means 'x' does not change, but 'y' changes.
The Slope Formula
The slope (often denoted by the letter 'm') of a line passing through two distinct points (x1, y1) and (x2, y2) is calculated using the following formula:
m = (y2 – y1) / (x2 – x1)
This formula can also be expressed as "rise over run," where "rise" is the vertical change (y2 – y1) and "run" is the horizontal change (x2 – x1).
How to Use the Slope Calculator
Our Slope Calculator simplifies this process for you. To use it:
- Enter Point 1 (x1, y1): Input the x-coordinate and y-coordinate of your first point into the respective fields.
- Enter Point 2 (x2, y2): Input the x-coordinate and y-coordinate of your second point into the respective fields.
- Click "Calculate Slope": The calculator will instantly compute the slope of the line connecting your two points and display the result.
Examples of Slope Calculation
Example 1: Positive Slope
Let's calculate the slope between Point A (2, 3) and Point B (6, 11).
- x1 = 2, y1 = 3
- x2 = 6, y2 = 11
m = (11 – 3) / (6 – 2)
m = 8 / 4
m = 2
A slope of 2 means that for every 1 unit the line moves horizontally to the right, it moves 2 units upwards.
Example 2: Negative Slope
Consider Point C (1, 7) and Point D (4, 1).
- x1 = 1, y1 = 7
- x2 = 4, y2 = 1
m = (1 – 7) / (4 – 1)
m = -6 / 3
m = -2
A slope of -2 means that for every 1 unit the line moves horizontally to the right, it moves 2 units downwards.
Example 3: Zero Slope (Horizontal Line)
Let's use Point E (0, 5) and Point F (8, 5).
- x1 = 0, y1 = 5
- x2 = 8, y2 = 5
m = (5 – 5) / (8 – 0)
m = 0 / 8
m = 0
A slope of 0 indicates a horizontal line.
Example 4: Undefined Slope (Vertical Line)
Consider Point G (3, 1) and Point H (3, 9).
- x1 = 3, y1 = 1
- x2 = 3, y2 = 9
m = (9 – 1) / (3 – 3)
m = 8 / 0
Division by zero is undefined in mathematics, hence the slope is Undefined. This represents a vertical line.
Use the calculator above to quickly find the slope for any two given points!