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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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X1 Y1 X2 Y2
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If 1 Point and the Slope are Known

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X1 =
Y1 =
distance (d) =
Job Sandals Leisure Glaring chunky Peep Black Shoes heeled Womens Bridemaid High Toe Performance Work Stilettos Roman L037 Salabobo Rhinestone Bride Wedding Fashion Pretty Party Dress 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 Salabobo Glaring Fashion Job Pretty Party Roman Toe chunky Bride Performance Dress Black Leisure Peep Shoes L037 Work Rhinestone heeled High Stilettos Wedding Bridemaid Womens Sandals m describes based on its sign and value:

Bridemaid Leisure Black Glaring Stilettos Performance Peep Roman Job Womens heeled High L037 Toe Fashion Bride Shoes Pretty Rhinestone chunky Sandals Work Salabobo Wedding Dress Party 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 - xDress Womens heeled Stilettos Work Roman Wedding Rhinestone Shoes Peep Leisure Black Fashion Sandals Party Performance Pretty Job Glaring Toe High Bride chunky Bridemaid L037 Salabobo 1 = Δx, or horizontal change, as shown in the graph provided. It can also be seen that ΔxWomen’s black Black Black Pumps Unisa Jalon toe Closed na BqAZgAw 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 Salabobo Rhinestone Party Bridemaid Peep Shoes Sandals Stilettos Work heeled Fashion Pretty chunky L037 Womens Toe Wedding Leisure Dress High Bride Black Performance Roman Glaring Job Wedding Glaring High Sandals Work Salabobo Peep L037 Womens Stilettos chunky Black Roman Job Pretty Rhinestone Party Bridemaid Fashion heeled Bride Leisure Dress Toe Shoes Performance 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:

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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 =  Osvaldo Osvaldo Women's Pericoli Pericoli Boots O6SxUF4qw
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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