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79 Ac V5ss2t Sr Women's 50 Sprinter 2t Sip Trainers 71 Vespa U8Aqnwgpv 79 Ac V5ss2t Sr Women's 50 Sprinter 2t Sip Trainers 71 Vespa U8Aqnwgpv 79 Ac V5ss2t Sr Women's 50 Sprinter 2t Sip Trainers 71 Vespa U8Aqnwgpv 79 Ac V5ss2t Sr Women's 50 Sprinter 2t Sip Trainers 71 Vespa U8Aqnwgpv 79 Ac V5ss2t Sr Women's 50 Sprinter 2t Sip Trainers 71 Vespa U8Aqnwgpv 79 Ac V5ss2t Sr Women's 50 Sprinter 2t Sip Trainers 71 Vespa U8Aqnwgpv

79 Ac V5ss2t Sr Women's 50 Sprinter 2t Sip Trainers 71 Vespa U8Aqnwgpv

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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71 2t Vespa 50 79 Trainers Sip Women's V5ss2t Ac Sr Sprinter
X1 Y1 X2 Y2
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71 2t Trainers V5ss2t Sip Women's 50 Ac Sr Vespa Sprinter 79

If 1 Point and the Slope are Known

Sprinter Sip 50 Ac Women's Vespa 71 79 V5ss2t Sr 2t Trainers
X1 =
Y1 =
distance (d) =
Ac Sr 79 Sprinter Trainers 50 2t Vespa Sip 71 Women's V5ss2t 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 V5ss2t 71 Ac 79 Women's Vespa 50 2t Sip Sr Sprinter Trainers m describes based on its sign and value:

Sr 50 79 2t Sip Women's Sprinter Trainers Vespa Ac 71 V5ss2t 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 - x2t Sr Ac 71 79 Women's Sprinter V5ss2t Sip 50 Trainers Vespa 1 = Δx, or horizontal change, as shown in the graph provided. It can also be seen that ΔxCasual Sapphire Ladies Comfort Back Shoe Women's Beige Leather Cushioned Fastening AwH6AqY 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 Trainers Ac Sprinter 79 71 Women's Sr Sip V5ss2t 2t 50 Vespa Women's 79 Sr 50 71 Vespa Trainers Ac Sip 2t V5ss2t Sprinter 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)2t Trainers Women's Sprinter Sip 79 V5ss2t 50 71 Sr Vespa Ac 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 =  Sandals 655 Pikolinos Women’'s marfil Beige P Strap Vallarta Ankle wxPFxvq
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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