Judith Black 001 Women’'s Loafers Semler schwarz Zv8qnwBy definition, the slope or gradient of a line describes its steepness, incline, or grade. 
If the 2 Points are Known
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Black Semler Women’'s Loafers Judith schwarz 001
If 1 Point and the Slope are Known
Black Judith schwarz 001 Women’'s Semler LoafersX_{1} =  
Y_{1} =  
distance (d) =  
001 Semler Black Women’'s Loafers Judith schwarz 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 Semler Loafers Judith 001 Black schwarz Women’'s m describes based on its sign and value:
 Black Semler Judith schwarz 001 Women’'s Loafers A line is increasing, and goes upwards from left to right when m > 0
 A line is decreasing, and goes downwards from left to right when m < 0
 A line has a constant slope, and is horizontal when m = 0 Blue Blue Face The Camp Mini North stripe Base Women’s Flip Flops R8vPFRxqw
 A vertical line has an undefined slope, since it would result in a fraction with 0 as the denominator. Refer to the equation provided below.
schwarz Women’'s Judith Loafers Semler 001 Black 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 = 

In the equation above, y_{2}  y_{1} = Δy, or vertical change, while x_{2}  x_{Black Judith Loafers schwarz Semler Women’'s 001 1} = Δx, or horizontal change, as shown in the graph provided. It can also be seen that Δx25530 Long Boots black Black Tamaris Women’s graphite g5ZqHwn1x and Δy are line segments that form a right triangle with hypotenuse d, with d being the distance between the points (x_{1}, y_{1}) and (x_{2}, y_{2}). Since Semler 001 Black Judith Loafers schwarz Women’'s Semler schwarz Judith Women’'s 001 Loafers 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 = √(x_{2}  x_{1})^{2} + (y_{2}  y_{1})^{Loafers Judith schwarz 001 Women’'s Black Semler 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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= 

d = √(6  3)^{2} + (8  4)^{2} = 5
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= 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 nonlinear 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.