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Slope

lastmod 2023-02-02created 2014-09-037 edits

Slope (North Korean standard language: bitaldo) is a number that expresses how steeply a straight line is inclined.

In a Cartesian coordinate system, the slope of a line can be expressed algebraically as follows. (m : slope of the line, Δx : change in x, Δy : change in y)

m = Δy / Δx

In geometry, the slope is equal to the value of tan θ.

m = Δy / Δx = tan θ

In a plane containing the X and Y axes, the slope of a line is usually denoted by the letter m and expressed as follows.

m = Δy / Δx = (y2 - y1) / (x2 - x1) = rise / run

Calculating the slope

Straight_line_definition.svg.png

Considering a line placed in a Cartesian coordinate system as in the graph on the right, the slope m can be calculated as follows.

This slope is also equal to the tangent of the angle Φ that the line makes where it crosses the x-axis.

m = Δy / Δx = b / a = tanΦ = sinΦ / cosΦ

See also

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