What is the Slope of a Line? Definition and Examples


What is the slope of a line? The slope of a line is the ratio of the rise to the run between any two points (x1, y1) and (x2, y2).

The rise is the distance straight up (or vertical distance) between the two points and the run is the horizontal distance between the two points. 

Slope of a line

The rise can also be called vertical change and the run can also be called horizontal change.

Different ways to define the slope of a line


Slope  = vertical change / horizontal change

Slope  = vertical distance / horizontal distance

Slope = rise / run

Slope = (y1 - y2) / (x1 - x2)

Example showing how to find the slope of a line


Use the two points shown in black in the figure above to find the slope of the line.

Slope  = rise / run = 6 / 4 = 3 / 2

Slope = (y1 - y2) / (x1 - x2)

(x1, y1) = (6, 9) and (x2, y2) = (2, 3)

Slope = (y1 - y2) / (x1 - x2)

Slope = (9 - 3) / (6 - 2)

Slope = (6) / (4) = 3 / 2

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