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Example:Find Angle Between Two Lines using Slope Concept

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The slope of a line in the plane is defined as the rise over the run, m = Δyx.


In mathematics, the slope or gradient of a line describes its steepness, incline, or grade. A higher slope value indicates a steeper incline.

The slope is (in the simplest of terms) the measurement of a line, and is defined as the ratio of the "rise" divided by the "run" between two points on a line, or in other words, the ratio of the altitude change to the horizontal distance between any two points on the line. Given two points (x1,y1) and (x2,y2) on a line, the slope m of the line is

(Our solved example in mathguru.com uses this concept)





Slope illustrated for y = (3/2) x − 1.

The slope of a line in the plane containing the x and y axes is generally represented by the letter m, and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line. This is described by the following equation:

(The delta symbol, "Δ", is commonly used in mathematics to mean "difference" or "change".)

Given two points (x1,y1) and (x2,y2), the change in x from one to the other is x2  x1 (run), while the change in yis y2  y1 (rise). Substituting both quantities into the above equation obtains the following:




The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.