Slope Calculator Using 2 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):

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1. What is the Slope Formula?

The slope formula calculates the steepness or incline of a line between two points in a coordinate system. It represents the rate of change between the two points.

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 (unitless)
\( x_1 \) — x-coordinate of first point (unitless)
\( y_1 \) — y-coordinate of first point (unitless)
\( x_2 \) — x-coordinate of second point (unitless)
\( y_2 \) — y-coordinate of second point (unitless)

Explanation: The formula calculates the ratio of vertical change to horizontal change between two points on a line.

3. Importance of Slope Calculation

Details: Slope is fundamental in mathematics, physics, engineering, and economics. It describes the direction and steepness of a line, representing rates of change in various applications from velocity to economic trends.

4. Using the Calculator

Tips: Enter coordinates for two distinct points. The calculator will compute the slope. If the x-coordinates are equal, the slope is undefined (vertical line).

5. Frequently Asked Questions (FAQ)

Q1: What does a positive slope indicate?
A: A positive slope indicates the line is rising from left to right, showing a positive relationship between variables.

Q2: What does a negative slope indicate?
A: A negative slope indicates the line is falling from left to right, showing an inverse relationship between variables.

Q3: What does a zero slope mean?
A: A zero slope means the line is horizontal, indicating no change in the y-value as x changes.

Q4: When is slope undefined?
A: Slope is undefined when the line is vertical (x₂ - x₁ = 0), which represents an infinite rate of change.

Q5: How is slope used in real-world applications?
A: Slope is used in various fields including physics (velocity), economics (marginal cost), engineering (gradient), and geography (terrain steepness).