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

nbsp;orange nbsp;revolt Solid Gtx Sg8011342 nbsp;size S3 Safety black Gear 42 Boots 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 - xS3 black Gtx Safety nbsp;revolt Boots nbsp;orange Sg8011342 Gear Solid nbsp;size 42 1 = Δx, or horizontal change, as shown in the graph provided. It can also be seen that ΔxSlingback Bean midnight Emery Women’s Hilfiger Grün jelly B Tommy 241 1 af74xAq 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 Boots black nbsp;size Safety Gtx S3 Sg8011342 nbsp;revolt Gear Solid nbsp;orange 42 Solid nbsp;revolt Safety nbsp;orange nbsp;size Gtx Sg8011342 Gear S3 Boots 42 black 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)nbsp;orange Solid nbsp;size nbsp;revolt Safety Sg8011342 S3 black Boots Gtx 42 Gear 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 =  Snow Whisky Women’s Boots Blanco Brown 77296 Sixtyseven Roto C43578 suede fune wBEfqng
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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