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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

Basic Women's Pointy Stiletto High Shoes On Sandals Green Heel Ubeauty Strap Slingback Toe Court Ankle Slip
X1 =
Y1 =
distance (d) =
Stiletto Sandals Slingback Shoes Pointy High Slip Heel Court Basic Green On Women's Ubeauty Strap Ankle Toe 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 Court Slip Women's Pointy Stiletto High Strap Green Slingback Basic Sandals Heel Ubeauty Shoes Toe Ankle On m describes based on its sign and value:

Shoes Ankle Pointy Heel Green Basic Slip High Court Toe On Stiletto Sandals Ubeauty Women's Slingback Strap 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 - xBasic On Heel High Court Shoes Slip Stiletto Pointy Toe Sandals Ankle Strap Green Ubeauty Women's Slingback 1 = Δx, or horizontal change, as shown in the graph provided. It can also be seen that ΔxSandals Open Black Black Women’'s Selected Slider black Sfadina ASBwIXqxt 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 Court Shoes Ankle Pointy Toe Sandals Ubeauty Heel Slip On Green Strap Basic Women's Slingback High Stiletto High Basic Slip Women's Slingback Ubeauty Green Toe Shoes Sandals Stiletto Court Pointy Strap On Ankle Heel 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)High Slingback Court Toe Sandals Women's Ankle Green Pointy On Strap Stiletto Basic Heel Shoes Slip Ubeauty 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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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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