direction of the line is increasing. Since |m| < 1, the incline is not very steep (incline < 45°). As another example, consider a line which runs through the points (4, 15) and (3, 21). Then, the slope of the line is Since the slope is negative, the direction of the line is decreasing. Since |m| > 1, this decline is fairly steep (decline > 45°). Algebra and geometry Examples For example, consider a line running through points (2,8) and (3,20). This line has a slope, , of One can then write the line's equation, in point-slope form: or: The angle θ between −90° and 90° that this line makes with the -axis is Consider the two lines: and . Both lines have slope . They are not the same line. So they are parallel lines. Consider the two lines and . The slope of the first line is . The slope of the second line is . The product of these two slopes is −1. So these two lines are perpendicular. Statistics In statistics, the gradient of the least-squares regression best-fitting line for a given sample of data may be written as: , This quantity m is called as the regression slope for the line . The quantity is Pearson's correlation coefficient, is the standard deviation of the y-values and is the standard deviation of the x-values. This may also be written as a ratio of covariances: Slope of a road or railway There are two common ways to describe the steepness of a road or railroad. One is by the angle between 0° and 90° (in degrees), and the other is by the slope in a percentage. See also steep grade railway and rack railway. The formulae for converting a slope given as a percentage into an angle in degrees and vice versa are: (this is the inverse function of tangent; see trigonometry) and where angle is in degrees and the trigonometric functions operate in degrees. For example, a slope of 100% or 1000‰ is an angle of 45°. A third way is to give one unit of rise in say 10, 20, 50 or 100 horizontal units, e.g. 1:10. 1:20, 1:50 or 1:100 (or "1 in 10", "1 in 20", etc.) Note that 1:10 is steeper than 1:20. For example, steepness of 20% means 1:5 or an incline with angle 11.3°. Roads and railways have both longitudinal