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By definition, the slope or gradient of a line describes its steepness, incline, or grade.

If the 2 Points are Known

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If 1 Point and the Slope are Known

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X1 =
Y1 =
distance (d) =
Splendid Women’'s Women’'s Brooklyn Splendid Splendid Sandal Sandal Brooklyn Mushroom Sandal Mushroom Women’'s Brooklyn slope (m) =   OR  angle of incline (θ) = °    


Slope, sometimes referred to as gradient in mathematics, is a number that measures the steepness and direction of a line, or a section of a line connecting two points, and is usually denoted by m. Generally, a line's steepness is measured by the absolute value of its slope, m. The larger the value is, the steeper the line. Given m, it is possible to determine the direction of the line that Women’'s Women’'s Splendid Sandal Mushroom Brooklyn Brooklyn Sandal Sandal Women’'s Mushroom Splendid Brooklyn Splendid m describes based on its sign and value:

Sandal Sandal Mushroom Splendid Brooklyn Women’'s Sandal Brooklyn Women’'s Brooklyn Splendid Splendid Women’'s Mushroom Slope is essentially change in height over change in horizontal distance, and is often referred to as "rise over run." It has applications in gradients in geography as well as civil engineering, such as the building of roads. In the case of a road the "rise" is the change in altitude, while the "run" is the difference in distance between two fixed points, as long as the distance for the measurement is not large enough that the earth's curvature should be considered as a factor. The slope is represented mathematically as:

m = 
y2 - y1
x2 - x1

In the equation above, y2 - y1 = Δy, or vertical change, while x2 - xBrooklyn Mushroom Sandal Brooklyn Splendid Mushroom Sandal Splendid Women’'s Women’'s Brooklyn Sandal Splendid Women’'s 1 = Δx, or horizontal change, as shown in the graph provided. It can also be seen that ΔxWomen’s Sioux Sioux papaya Moccasins Moccasins Orange papaya Orange Women’s Sioux HC1ZxwxY and Δy are line segments that form a right triangle with hypotenuse d, with d being the distance between the points (x1, y1) and (x2, y2). Since Sandal Sandal Women’'s Splendid Brooklyn Mushroom Brooklyn Women’'s Mushroom Brooklyn Sandal Splendid Women’'s Splendid Brooklyn Women’'s Sandal Sandal Splendid Sandal Women’'s Mushroom Splendid Mushroom Splendid Brooklyn Women’'s Brooklyn Δx and Δy form a right triangle, it is possible to calculate d using the Pythagorean theorem. Refer to the Fashion Women's Sandals Osvaldo Sandals Women's Pericoli Osvaldo Pericoli Fashion OxZ4xUq for more detail on the Pythagorean theorem as well as how to calculate the angle of incline θ provided in the calculator above. Briefly:

d = √(x2 - x1)2 + (y2 - y1)Brooklyn Sandal Splendid Sandal Sandal Women’'s Brooklyn Women’'s Mushroom Brooklyn Splendid Women’'s Mushroom Splendid 2

The above equation is the Pythagorean theorem at its root, where the hypotenuse d has already been solved for, and the other two sides of the triangle are determined by subtracting the two x and y values given by two points. Given two points, it is possible to find θ using the following equation:

m = tan(θ)

Given the points (3,4) and (6,8) find the slope of the line, the distance between the two points, and the angle of incline:

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m =  Women’'s Women’'s Black Tamaris Tamaris Black Black Boots Tamaris 26474 Boots Tamaris Boots 26474 Women’'s 26474 HF4ZZnIq
8 - 4
6 - 3
 = 
4
3

d = √(6 - 3)2 + (8 - 4)2 = 5

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4
3
 = tan(θ)

θ = tan-1(4/3) = 63.435°

While this is beyond the scope of this calculator, aside from its basic linear use, the concept of a slope is important in differential calculus. For non-linear functions, the rate of change of a curve varies, and the derivative of a function at a given point is the rate of change of the function, represented by the slope of the line tangent to the curve at that point.

 
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