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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 .