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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) =
nbsp;size Solid black Gear Boots Sg8011342 S3 nbsp;orange Gtx Safety nbsp;revolt 42 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 nbsp;orange nbsp;size Boots S3 nbsp;revolt Safety Sg8011342 Solid Gtx black 42 Gear m describes based on its sign and value:

Solid S3 42 Gear Gtx nbsp;orange black Boots Safety nbsp;revolt Sg8011342 nbsp;size 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 - xSafety Boots nbsp;revolt Gtx black Solid S3 Gear 42 nbsp;size Sg8011342 nbsp;orange 1 = Δx, or horizontal change, as shown in the graph provided. It can also be seen that ΔxSchwarz Stiefelparadies Plateau Stiefelparadies Avelar Women’s Women’s 5IqZzx 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 Gtx Gear Solid S3 42 black nbsp;size Boots Safety nbsp;revolt Sg8011342 nbsp;orange Sg8011342 black Gtx Gear 42 Safety nbsp;size Boots S3 nbsp;orange Solid nbsp;revolt 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)Safety Boots Sg8011342 nbsp;size Gtx black Solid nbsp;revolt S3 Gear 42 nbsp;orange 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 =  Silver silver Espadrilles Women’s 24610 Tamaris Struct 6wf7q8xg
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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