Slope Calculator

Calculate the slope of a line between two points, find the equation of a line, and analyze linear relationships. Perfect for algebra, geometry, and coordinate geometry problems.

Calculate Slope

Calculation Method

Point 1 (x₁, y₁)

Point 2 (x₂, y₂)

Quick Examples

Slope Properties

Direction:Rising (positive)

Steepness:Very steep

Angle with X-axis:63.43°

Perpendicular slope:-0.5000

Calculation Results

Slope (m):

2.0000

Rise over Run:

4/2

Distance between points:

4.4721

Midpoint:

(1, 2)

Line Equations

Slope-Intercept Form:

y = 2.0000x

Point-Slope Form:

y - 0 = 2.0000(x - 0)

Standard Form:

2.0000x + -1y = 0.0000

Step-by-Step Calculation

Step 1: Identify the points

Point 1: (0, 0), Point 2: (2, 4)

Step 2: Apply the slope formula

m = (y₂ - y₁) / (x₂ - x₁)

Step 3: Substitute the values

m = (4 - 0) / (2 - 0)

Step 4: Calculate the result

m = 4 / 2 = 2.0000

How to Use This Calculator

This slope calculator helps you find the slope of a line and analyze linear relationships using various methods.

Choose your calculation method from the dropdown menu
Enter the required values based on your selected method
View the calculated slope and line properties
Examine different forms of the line equation
Follow the step-by-step calculation to understand the process

Understanding Slope

What is Slope?

Slope measures the steepness and direction of a line. It represents the rate of change between two variables, showing how much the y-value changes for each unit change in the x-value.

Slope Formula

The slope formula between two points (x₁, y₁) and (x₂, y₂) is:

m = (y₂ - y₁) / (x₂ - x₁)

Types of Slopes

Positive Slope: Line rises from left to right (m > 0)
Negative Slope: Line falls from left to right (m < 0)
Zero Slope: Horizontal line (m = 0)
Undefined Slope: Vertical line (division by zero)

Slope Relationships

Parallel Lines: Have equal slopes (m₁ = m₂)
Perpendicular Lines: Have negative reciprocal slopes (m₁ × m₂ = -1)
Angle with X-axis: θ = arctan(m)

Example Calculations

Example 1: Positive Slope

Find the slope between points (1, 2) and (3, 8).

Solution: m = (8 - 2) / (3 - 1) = 6 / 2 = 3

The line rises 3 units for every 1 unit to the right.

Example 2: Negative Slope

Find the slope between points (0, 5) and (4, 1).

Solution: m = (1 - 5) / (4 - 0) = -4 / 4 = -1

The line falls 1 unit for every 1 unit to the right.

Example 3: From Standard Form

Find the slope of the line 3x + 2y = 6.

Solution: Rearrange to y = mx + b form

2y = -3x + 6 → y = -3/2 x + 3

Therefore, m = -3/2

Frequently Asked Questions

What does undefined slope mean?

Undefined slope occurs when the denominator (x₂ - x₁) equals zero, meaning the line is vertical. Vertical lines have no finite slope value because they rise infinitely for zero horizontal change.

How do I find perpendicular slope?

The perpendicular slope is the negative reciprocal of the original slope. If the original slope is m, the perpendicular slope is -1/m. For example, if m = 2, the perpendicular slope is -1/2.

Can slope be greater than 1?

Yes, slope can be any real number. A slope greater than 1 means the line is steep, rising more than 1 unit vertically for each unit horizontally. A slope between 0 and 1 indicates a gentler incline.