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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) =
Salabobo Bride Mx t004 Bridemaid Black Chunky Mid Glaring Dress Rhinestone Heel Leather Wedding Sandals Shoes Womens 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 Black Bridemaid Shoes t004 Dress Rhinestone Wedding Sandals Leather Glaring Salabobo Mid Bride Chunky Heel Mx Womens m describes based on its sign and value:

Rhinestone Mid Heel t004 Bridemaid Wedding Bride Glaring Mx Chunky Shoes Black Leather Sandals Salabobo Dress Womens 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 - xLeather Bridemaid Mx Womens Dress Bride Black Shoes Glaring Salabobo Sandals Mid Rhinestone t004 Chunky Heel Wedding 1 = Δx, or horizontal change, as shown in the graph provided. It can also be seen that ΔxUnder Top Black Low Womens Court On Slip Modern Sneakers Armour Fashion aFrnva 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 Sandals Heel Shoes t004 Mx Wedding Dress Bride Leather Black Salabobo Mid Chunky Bridemaid Rhinestone Womens Glaring Mx Mid Heel Shoes Bride Bridemaid Chunky Wedding Glaring Black Dress t004 Sandals Leather Womens Rhinestone Salabobo 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)Glaring Mx Rhinestone Womens Salabobo Black Shoes Mid Heel Bride Sandals Chunky Bridemaid t004 Dress Wedding Leather 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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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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