Slope from Two Points Calculator

Use this calculator to quickly find the slope (also known as the gradient) of a straight line when you know the coordinates of any two points on that line. It's a fundamental concept in algebra and geometry.

X₁ Coordinate

Enter the x-coordinate of the first point.

Y₁ Coordinate

Enter the y-coordinate of the first point.

X₂ Coordinate

Enter the x-coordinate of the second point.

Y₂ Coordinate

Enter the y-coordinate of the second point.

How it works

Use this calculator to quickly find the slope (also known as the gradient) of a straight line when you know the coordinates of any two points on that line. It's a fundamental concept in algebra and geometry.

The Formula

The slope 'm' between two points (x₁, y₁) and (x₂, y₂) is calculated using the formula: m = (y₂ - y₁) / (x₂ - x₁) This represents the 'rise over run' of the line.

Worked Example

Example: Finding the Slope
Let's find the slope of a line passing through point A (3, 5) and point B (7, 13). Here, x₁=3, y₁=5, x₂=7, y₂=13. m = (13 - 5) / (7 - 3) m = 8 / 4 m = 2 The slope of the line is 2.

Tips, Assumptions & Limitations

Remember that a positive slope means the line rises from left to right.
A negative slope means the line falls from left to right.
A slope of zero indicates a horizontal line.
An undefined slope means the line is vertical.

FAQ

Slope, or gradient, measures the steepness and direction of a line. It tells you how much the y-value changes for every unit change in the x-value. A higher absolute slope means a steeper line.

Slope is crucial for understanding linear equations, graphing, and real-world applications like rates of change (speed, growth). It helps describe relationships between two variables.

Yes, if the x-coordinates of your two points are identical, the calculator will correctly identify the line as vertical and state that the slope is undefined.