Slope Calculator Desmos

Slope Formula:

\[ m = \frac{y₂ - y₁}{x₂ - x₁} \]

x₁ (x-coordinate of first point):

unitless

y₁ (y-coordinate of first point):

unitless

x₂ (x-coordinate of second point):

unitless

y₂ (y-coordinate of second point):

unitless

Slope (m):

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1. What is Slope?

Slope is a measure of the steepness of a line, representing the ratio of the vertical change (rise) to the horizontal change (run) between two points on a line. It describes the direction and steepness of the line.

2. How Does the Calculator Work?

The calculator uses the slope formula:

\[ m = \frac{y₂ - y₁}{x₂ - x₁} \]

Where:

\( m \) — Slope of the line (unitless)
\( x₁ \) — x-coordinate of the first point (unitless)
\( y₁ \) — y-coordinate of the first point (unitless)
\( x₂ \) — x-coordinate of the second point (unitless)
\( y₂ \) — y-coordinate of the second point (unitless)

Explanation: The formula calculates the rate of change between two points on a coordinate plane. A positive slope indicates an upward trend, negative slope indicates a downward trend, and zero slope indicates a horizontal line.

3. Importance of Slope Calculation

Details: Slope calculation is fundamental in mathematics, physics, engineering, and data analysis. It helps determine rates of change, trends in data, and the angle of inclination in various applications.

4. Using the Calculator

Tips: Enter the coordinates of two distinct points. The calculator will compute the slope. Avoid entering identical x-coordinates as this results in division by zero (undefined slope).

5. Frequently Asked Questions (FAQ)

Q1: What does a slope of zero mean?
A: A slope of zero indicates a horizontal line, meaning there is no vertical change between the points.

Q2: What does an undefined slope mean?
A: An undefined slope occurs when the denominator is zero (x₂ = x₁), indicating a vertical line.

Q3: Can slope be negative?
A: Yes, a negative slope indicates that the line is decreasing from left to right.

Q4: How is slope used in real-world applications?
A: Slope is used in various fields including physics (velocity), economics (marginal cost), and engineering (gradient).

Q5: What is the difference between slope and gradient?
A: Slope typically refers to the steepness of a line in two dimensions, while gradient is a vector quantity that represents the slope in multiple dimensions.