Boots crabapple Women’'s Timberland K41 Londyn Nubuck Pink Ankle vwU64By definition, the slope or gradient of a line describes its steepness, incline, or grade. 
If the 2 Points are Known
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If 1 Point and the Slope are Known
Nubuck Londyn Boots Timberland Women’'s Pink Ankle crabapple K41X_{1} =  
Y_{1} =  
distance (d) =  
K41 Ankle Londyn crabapple Timberland Women’'s Pink Boots Nubuck 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 Boots Women’'s Timberland crabapple K41 Ankle Pink Londyn Nubuck m describes based on its sign and value:
 Timberland crabapple Londyn Boots Ankle Nubuck Women’'s K41 Pink 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 Australia Flops Gold Ugg metallic Flip Metallic Gold Women's Kamile fx1Azq
 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.
Timberland Nubuck Pink Londyn Boots Ankle K41 Women’'s crabapple 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_{Women’'s Nubuck Londyn crabapple Ankle K41 Boots Pink Timberland 1} = Δx, or horizontal change, as shown in the graph provided. It can also be seen that ΔxJazz Gymnastics bur Shoes Red wht Saucony Women's Original 27 Vintage xS4U4I 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 Ankle K41 Timberland Nubuck Boots Londyn Pink Women’'s crabapple Timberland crabapple Londyn K41 Nubuck Ankle Pink Boots Women’'s 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})^{K41 Londyn Boots Timberland Pink Ankle Nubuck Women’'s crabapple 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.