Slope of the Line Calculator Given Two Points

Slope Formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

x₁ (x-coordinate of first point):

y₁ (y-coordinate of first point):

x₂ (x-coordinate of second point):

y₂ (y-coordinate of second point):

Slope (m):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Slope of a Line?

The slope of a line measures its steepness and direction. It represents the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.

2. How Does the Calculator Work?

The calculator uses the slope formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Where:

\( m \) — Slope of the line (unitless)
\( x_1, y_1 \) — Coordinates of the first point
\( x_2, y_2 \) — Coordinates of the second point

Explanation: The formula calculates how much the y-value changes for each unit change in the x-value between two points on a line.

3. Importance of Slope Calculation

Details: Slope is fundamental in mathematics, physics, engineering, and economics. It describes rates of change, inclines, gradients, and relationships between variables in linear equations.

4. Using the Calculator

Tips: Enter coordinates for two distinct points. The calculator will compute the slope. If the line is vertical (x₂ = x₁), the slope is undefined.

5. Frequently Asked Questions (FAQ)

Q1: What does a positive slope indicate?
A: A positive slope indicates the line rises as it moves from left to right.

Q2: What does a negative slope indicate?
A: A negative slope indicates the line falls as it moves from left to right.

Q3: What does a zero slope mean?
A: A zero slope indicates a horizontal line with no vertical change.

Q4: When is slope undefined?
A: Slope is undefined for vertical lines where x₂ = x₁ (division by zero).

Q5: Can slope be used in real-world applications?
A: Yes, slope is used in various applications including calculating gradients in construction, determining rates in economics, and analyzing trends in data science.