Understanding the Slope of a Line

The slope of a line is a measure of its steepness and direction. It describes how much the line rises or falls vertically for every unit it moves horizontally. A higher absolute value of slope indicates a steeper line.

The Slope Formula

The slope (often denoted by m) of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:

m = (y₂ - y₁) / (x₂ - x₁)

Example Calculation

Let's calculate the slope of a line passing through points (2, 3) and (6, 11).

• x₁ = 2, y₁ = 3
• x₂ = 6, y₂ = 11

Using the formula:

m = (11 - 3) / (6 - 2)

m = 8 / 4

m = 2

The slope of the line is 2.

Interpreting Slope Values

• Positive Slope (m > 0): The line goes upwards from left to right, indicating a positive relationship between x and y.
• Negative Slope (m < 0): The line goes downwards from left to right, indicating a negative relationship between x and y.
• Zero Slope (m = 0): The line is perfectly horizontal. This means there is no change in y as x changes.
• Undefined Slope (x₂ - x₁ = 0): The line is perfectly vertical. This occurs when the x-coordinates of the two points are the same, making the denominator of the formula zero.