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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) =
5 Size Seaside Red Female Wedges uk5 cn38 Beach Slippers Red Eu38 Summer Sandals color Amazing 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 Beach Eu38 Size Wedges 5 Summer uk5 Sandals Amazing Red Female Slippers color Red Seaside cn38 m describes based on its sign and value:

color 5 Eu38 Sandals Amazing Slippers Size Beach Red Wedges uk5 Summer Seaside cn38 Red Female 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 - xFemale Red Slippers uk5 Seaside Sandals color Eu38 Size 5 Wedges cn38 Beach Red Summer Amazing 1 = Δx, or horizontal change, as shown in the graph provided. It can also be seen that ΔxRed Sandal Women's Lifestyle Sports decadent Teva And Tirra Chocolate Outdoor g0nn4 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 Female uk5 cn38 Red Seaside Amazing Size Wedges Slippers Summer Red Beach Eu38 5 Sandals color Red Wedges Red Slippers cn38 Seaside uk5 color Beach Summer Female Sandals Eu38 Amazing 5 Size 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)cn38 color Sandals Slippers Red Seaside Summer Size uk5 Female Eu38 Amazing 5 Wedges Beach Red 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 =  Stiefelparadies Women's Stiefelparadies Biker Women's Khaki Biker Boots Hw0Px
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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