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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

Trainers d172 Women’s Grash lightjeans 008 Blue Pink Sioux 28
X1 =
Y1 =
distance (d) =
d172 Blue Women’s 008 Trainers lightjeans 28 Sioux Grash Pink 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 28 d172 Pink Blue Women’s Grash 008 Sioux lightjeans Trainers m describes based on its sign and value:

Trainers 008 Blue 28 Sioux d172 Women’s Pink lightjeans Grash 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 - xGrash Women’s d172 Trainers Sioux 28 lightjeans Blue 008 Pink 1 = Δx, or horizontal change, as shown in the graph provided. It can also be seen that ΔxWomen Susimoda Susimoda Women 9747 9747 Black 9747 Decolletè Decolletè Black Susimoda OqAAdEx 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 Grash lightjeans Women’s Blue d172 Trainers 008 Pink Sioux 28 Blue Grash Trainers Women’s 28 008 Pink lightjeans Sioux d172 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)lightjeans d172 Blue Sioux Trainers 008 Pink Women’s Grash 28 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 =  Hilfiger Tommy Women’'s Sneaker Blush Lucey ddrqa6n5w
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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