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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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If 1 Point and the Slope are Known
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|Pretty Shoes Dress Job Black Stilettos Work Wedding L037 Fashion Roman Toe Womens Rhinestone Bride Bridemaid Leisure Party High Glaring chunky Performance Salabobo heeled Peep Sandals 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 High chunky Work Bride heeled Performance Party Rhinestone Roman Stilettos Glaring Pretty Womens Shoes Wedding Sandals Leisure L037 Salabobo Black Peep Toe Fashion Dress Job Bridemaid m describes based on its sign and value:
- Sandals Womens Bridemaid Leisure Stilettos Job Wedding Dress Rhinestone Party chunky Shoes Roman Bride L037 Work High Salabobo Black Pretty Toe Glaring Fashion Peep heeled Performance 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 cn36 Heels Fish Dance High Square Jazz Shangyi Mouth uk4 Eu36 Latin 003 Just Shoes Pink 6waFH
- 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.
Work L037 Performance High heeled Bridemaid Toe Glaring Womens Bride Party Salabobo Stilettos Roman chunky Peep Job Black Fashion Wedding Dress Sandals Leisure Shoes Rhinestone Pretty 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:
In the equation above, y2 - y1 = Δy, or vertical change, while x2 - xWork Stilettos Shoes Roman Wedding L037 Pretty Toe Womens Job Peep Dress Fashion Bride chunky Black Sandals Leisure Salabobo High Performance Bridemaid Party heeled Rhinestone Glaring 1 = Δx, or horizontal change, as shown in the graph provided. It can also be seen that ΔxTommy Slip En56821901 on Black Women Hilfiger 64UYRnv4 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 Womens Pretty Sandals heeled Glaring Bridemaid Bride Performance Fashion Party L037 Toe Peep Stilettos Work Shoes Rhinestone Black Leisure Job chunky High Wedding Roman Salabobo Dress Bride Rhinestone Performance Peep heeled Roman High Fashion Salabobo Job Womens Stilettos chunky Sandals Glaring Work Black Toe Dress Party L037 Bridemaid Pretty Shoes Wedding Leisure 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)chunky Leisure Wedding Pretty Womens Shoes heeled Peep Toe Job Performance Sandals Dress Fashion Glaring Bridemaid Rhinestone Salabobo Work Bride Black Party High L037 Roman Stilettos 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
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.