Geometry Tool

Slope Calculator

Find the slope (m) of a line passing through two points.

Point 1

Point 2

Σ The Formula

m = (y₂ - y₁) / (x₂ - x₁)

Real World Examples

Positive Slope
(1,2) to (3,6) → m = (6-2)/(3-1) = 2
Negative Slope
(0,5) to (5,0) → m = (0-5)/(5-0) = -1
Horizontal Line
(2,3) to (5,3) → m = 0 (no rise)
Vertical Line
(4,1) to (4,5) → m = undefined (no run)

# About This Calculator

Slope is a fundamental concept in algebra and geometry that measures the steepness and direction of a line. Often described as "rise over run," it tells you how much the y-value changes for each unit change in x. A slope of 2 means the line rises 2 units for every 1 unit it runs horizontally.

Slope appears in countless real-world contexts: the grade of a road (6% grade = 0.06 slope), the pitch of a roof, the rate of change in economics (marginal cost), velocity in physics (distance over time), and trend analysis in data science. Understanding slope helps you interpret graphs, predict trends, and solve practical problems.

The formula m = (y₂ - y₁) / (x₂ - x₁) calculates slope from any two points on a line. Positive slopes rise from left to right, negative slopes fall, zero slope means horizontal (flat), and undefined slope means vertical (straight up). The steeper the line, the larger the absolute value of the slope.

This calculator handles all cases including horizontal lines (slope = 0) and vertical lines (undefined slope). It also provides the slope-intercept form (y = mx + b) and point-slope form, making it perfect for graphing, writing equations, and analyzing linear relationships.

How To Use

  1. Enter coordinates for two points.
  2. Click Calculate.

Frequently Asked Questions

What does a negative slope mean?+

A negative slope means the line goes downward from left to right. As x increases, y decreases. For example, a slope of -2 means for every 1 unit you move right, the line drops 2 units. Common in declining trends, downhill roads, or decreasing functions.

What's the difference between slope 0 and undefined slope?+

Slope 0 is a horizontal line (flat, like y = 3). Undefined slope is a vertical line (straight up/down, like x = 5). Zero slope has no rise; undefined slope has no run (division by zero).

How do I find the equation of a line from slope?+

Use point-slope form: y - y₁ = m(x - x₁), or slope-intercept form: y = mx + b. If you have slope m and a point (x₁, y₁), plug them into point-slope form. To get y-intercept b, solve for y when x = 0.

What does slope represent in real life?+

Slope represents rate of change: speed (distance/time), cost per item (price/quantity), grade of a hill (rise/run), efficiency (output/input), or any relationship where one variable changes relative to another. Steeper slope = faster change.

Are parallel lines related to slope?+

Yes! Parallel lines have identical slopes. Perpendicular lines have slopes that are negative reciprocals (if one is 2, the other is -1/2). This is crucial for geometry, coordinate proofs, and understanding line relationships.

Is Slope Calculator free to use?+

Yes, Slope Calculator on Matheric is completely free to use. We believe in accessible education and utility for everyone.

About

Slope is a fundamental concept in algebra and geometry that measures the steepness and direction of a line. Often described as "rise over run," it tells you how much the y-value changes for each unit change in x. A slope of 2 means the line rises 2 units for every 1 unit it runs horizontally.

Slope appears in countless real-world contexts: the grade of a road (6% grade = 0.06 slope), the pitch of a roof, the rate of change in economics (marginal cost), velocity in physics (distance over time), and trend analysis in data science. Understanding slope helps you interpret graphs, predict trends, and solve practical problems.

The formula m = (y₂ - y₁) / (x₂ - x₁) calculates slope from any two points on a line. Positive slopes rise from left to right, negative slopes fall, zero slope means horizontal (flat), and undefined slope means vertical (straight up). The steeper the line, the larger the absolute value of the slope.

This calculator handles all cases including horizontal lines (slope = 0) and vertical lines (undefined slope). It also provides the slope-intercept form (y = mx + b) and point-slope form, making it perfect for graphing, writing equations, and analyzing linear relationships.

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