Relationship between Slope and Angle

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Slope and Angel

Slope of a Straight Line

Let l is a straight line joining two points P1(x1, y1) and P2(x2, y2). The slope of l is given by

(y2 - y1)/(x2 - x1)... (1)

Thus, slope of a straight line is the ratio of the difference of ordinates of two points to the difference of abscissas of the two points. Theoretically, slope tells that for one unit increase in the quantity measured on the x-axis, by how many units the quantity measured on the y-axis increases or decreases (Bello, Britton and & Kaul, 2008). In polar coordinates the slope of a line making an angle a with the x-axis can be measured as

slope = tan(a)... (2)

In equation of a straight line the slope is written as

y = mx + c... (3)

Where y is the quantity measured on the y axis, m is the slope, x is the quantity measured on the x-axis, and c is the y-intercept. Solving equation (3) for m

m = (y - c)/x

It is to note that the slope of a horizontal line (x-axis) is zero and the slope of a vertical line (y-axis) is infinite.

Sign of Slope

The positive sign of the slope represents that y increases for one unit increase in x and the negative sign of the slope represents that y decreases for one unit increase in x. In other words, positive slope means that y is directly proportional to x and negative slope means that y is inversely proportional to x.

Angle of Line

Angel between two lines is the angular distance between them in counter clockwise motion. From equation (2) it can be seen that the angel between a straight line and the x-axis is the arctangent of the line's slope (Haighton, Phillips, et al., 2004). Mathematically,

a = tan-1(m)... (4)

Where T ...