In topography, the slope of a hill, mountain, road or anything else inclined, can be expressed as a percentage or an angle. In vehicular engineering, various landbased designs (cars, SUVs, trucks, trains, etc.) are rated for their ability[?] to "climb" the slope of terrain[?]. For a train that is typically much less than for cars.

Definition of a Slope It is defined as the change in y divided by the corresponding change in x (if the horizontal axis is the xaxis and the vertical axis is the yaxis), often written as
Note that it doesn't matter which two points on the line you pick, or in which order you use them: the same line will always have the same slope. Curves have "accelerating" slopes and one can use calculus to determine such slopes.
Example 1 Suppose a line runs through two points: P(13,8) and Q(1,2). By dividing the difference in ycoordinates by the difference in xcoordinates, one can obtain the slope of the line:
Δy y_{1}  y_{2} 8  2 6 1 m = —— = ———————— = ——————— = ——— = —— Δx x_{1}  x_{2} 13  1 12 2
The slope is 1/2 = 0.5.
Example 2 If a line runs through the points (4, 15) and (3, 21) then m = (21  15) / (3  4) = 6 / 1 = 6.
Geometry The larger the slope, the steeper the line. A horizontal line has slope 0, a 45° rising line has a slope of +1, and a 45° falling line has a slope of 1. The slope of a vertical line is not defined (it does not make sense to define it as +∞, because it might just as well be defined as ∞).
The angle θ a line makes with the positive x axis is closely related to the slope m via the tangent function:
Two lines are parallel if and only if their slopes are equal; they are perpendicular (i.e. they form a right angle) if and only if the product of their slopes is 1.
If the equation of the line is given in the form
If you know the slope m of a line and a point (x_{0}, y_{0}) on the line, then you can find the equation of the line using the pointslope formula:
For example, consider a line running through the points (2, 8) and (3, 20). This line has a slope, m, of (20  8) / (3  2) = 12. One can then write the line's equation, in pointslope form: y  8 = 12(x  2) = 12x  24; or: y = 12x  16
The concept of a slope is central to differential calculus; which deals with curved functions. Unlike straight functions, the slope of curved functions varies at different points. This slope is often referred to as a derivative. To find the slope of a curved function, at a given point, one must find a line which is tangent to said function, at said point. The slope of said tangential line is equal to the slope of said function at said point.
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