Overview
The slope of a line describes its steepness and direction. It is the vertical change divided by the horizontal change between any two points on the line, and it connects to the line's angle and its slope-intercept equation.
Formula
m = (y₂ − y₁) ÷ (x₂ − x₁), then y = mx + b where b = y₁ − mx₁.
How it works
Read both points
Identify x₁, y₁, x₂ and y₂.
Compute both changes
Vertical = y₂ − y₁, horizontal = x₂ − x₁.
Divide
Slope = vertical change ÷ horizontal change.
Write the equation
Use the slope and y-intercept.
Worked examples
Example 1: (1, 2) and (3, 6)
m = 4 ÷ 2 = 2, and the equation is y = 2x.
Example 2: (0, 5) and (4, 1)
m = −4 ÷ 4 = −1, and the equation is y = −x + 5.
Frequently asked questions
What does a zero slope mean?
The line is horizontal, since y does not change as x changes.
What is the slope of a vertical line?
Undefined, because the horizontal change is zero.
How do I find the slope of a perpendicular line?
It is the negative reciprocal of the original slope.
This calculator is for educational and informational purposes only and is not a substitute for professional advice.