Calculate Slope of A Line in Degrees

What is Slope?

Slope is a measure of the steepness and direction of a line. It is often represented by the letter "m" and is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

The slope can be positive, negative, zero, or undefined. A positive slope indicates an upward trend, while a negative slope indicates a downward trend. A zero slope means the line is horizontal, and an undefined slope means the line is vertical.

Slope in Degrees

While slope is typically expressed as a ratio, it can also be converted to degrees to represent the angle of inclination of the line. This is particularly useful in fields like physics and engineering where angles are more intuitive.

The arctangent function (arctan) converts the slope ratio to an angle in radians, which is then converted to degrees by multiplying by 180/π.

How to Calculate the Slope in Degrees

1. Identify two points on the line: (x₁, y₁) and (x₂, y₂).
2. Calculate the slope (m) using the formula: m = (y₂ - y₁) / (x₂ - x₁).
3. Convert the slope to degrees using the formula: θ = arctan(m) × (180/π).
4. Interpret the result: a positive angle means the line rises to the right, while a negative angle means it falls to the right.

Example Calculation

Let's calculate the slope of a line passing through the points (2, 3) and (5, 7) in degrees.

1. Calculate the slope: m = (7 - 3) / (5 - 2) = 4 / 3 ≈ 1.333.
2. Convert to degrees: θ = arctan(1.333) × (180/π) ≈ 53.13°.

The line has an angle of inclination of approximately 53.13 degrees.