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Slope of a Line

Definition of Slope

The slope of a line is the ratio of the rise to the run when moving from any point on the line to any other point on the line. This ratio is a number that describes the steepness of the line.

By tradition, the letter m is used to represent the slope of a line.

Definition â€” Slope

The slope of the line between two points, (x₁, y₁) and (x₂, y₂), is given by

where x₁ ≠ x₂.

Example

Find the slope of the line through the points (-2, 1) and (3, 5).

Solution

It does not matter which point we choose for (x₁, y₁).

For example,

let (x₁, y₁) = (-2, 1) and (x₂, y₂) = (3, 5).	m
Substitute the values in the slope formula.
Simplify.
The slope of the line is . To move from (-2, 1) to (3, 5), the ratio of rise to run is .
We obtain the same slope if we choose (3, 5) for (x₁, y₁) and (-2, 1) for (x₂, y₂).	m
Substitute the values in the slope formula.
Simplify.

To move from (3, 5) to (-2, 1), the ratio of rise to run is .