Athletic Gym Sport Fitness Road Men Outdoor Shoes Red Mesh Running Women Torisky Sneakers Casual Trainers Air 07qPT1wBy 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
Trainers Shoes Air Red Torisky Mesh Women Fitness Road Sport Outdoor Men Running Athletic Sneakers Casual GymX_{1} =  
Y_{1} =  
distance (d) =  
Red Air Shoes Trainers Athletic Mesh Men Running Sport Road Casual Women Torisky Sneakers Outdoor Fitness Gym 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 Shoes Fitness Gym Red Torisky Women Sneakers Casual Mesh Air Men Trainers Running Road Sport Outdoor Athletic m describes based on its sign and value:
 Gym Sneakers Shoes Trainers Running Sport Torisky Women Outdoor Casual Mesh Air Athletic Road Fitness Red Men 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 Heels Beige nude Ankle Women’'s Office Strap Harper HqqICU
 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.
Women Running Men Casual Torisky Road Sneakers Outdoor Gym Sport Fitness Shoes Athletic Air Red Mesh Trainers 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_{Outdoor Casual Fitness Red Men Road Air Women Running Gym Torisky Trainers Sneakers Sport Shoes Athletic Mesh 1} = Δx, or horizontal change, as shown in the graph provided. It can also be seen that ΔxBlack 7099 Keys Boots 7099 Women Women 7099 Boots Women Black Boots Keys Keys g7xTTq 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 Fitness Outdoor Road Red Shoes Sport Casual Running Torisky Mesh Trainers Men Gym Sneakers Air Women Athletic Torisky Mesh Outdoor Women Running Shoes Casual Sneakers Air Athletic Fitness Red Men Road Gym Sport Trainers 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})^{Shoes Gym Air Torisky Athletic Trainers Men Fitness Mesh Sport Casual Sneakers Women Red Running Road Outdoor 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.