SLOPE OF THE LINE



In this page slope of the line we are going to see methods of finding the slope-of-the-line.We have several method to find slope. We need to use one of the method depending upon the given details.First let us look into the definition.Let a straight line cut the X axis at A. The angle theta between the straight line and the positive direction of the X axis when measured in the anticlockwise direction is called angle of inclination.The tangent of the angle of inclination is called slope or gradient of the line.

In the above figure AB is the part of the line above the x axis and if angle XAB = theta then slope = tan theta.

Important note:

(i)  The angle of inclination of x axis is 0 degree.

(ii)  The angle of inclination of every line parallel to the x axis is 0 degree.

(iii)  The angle of inclination of y-axis is 90 degree

(iv)  The angle of inclination of every line parallel to the y axis is 90 degree.

Formulas to find the slope of the straight line. The English alphabet "m" is used to denote slope.

(i)  m = tan θ

(ii) m = (y2 - y1)/(x2 - x1)

(iii)   m = - coefficient of x / coefficient of y

(iv)  If the given line is in the form of y = m x + b.The number which is instead of m is the slope

We will be use one of these formulas depending on the given details.If we are given the angle of inclination then we have to consider that angle as theta,then we have to apply the value in the first formula instead of theta.So we will get the required slope.If we have two points on the line is given then we have to use the second method to find the slope.The third and fourth method are being used when the equation of the line is given and we are asking to find slope of the line.

Example 1:

Find the slope whose inclination with x axis is 60 degree

Solution:

Here the angle of inclination is given so we have to consider this as theta

                                   Slope = tan (theta)

                                   Slope = tan (60 degree)                                

Therefore m = √ 3

Example 2:

Find the slope passing through the points (7,5) and (1,3)

Solution:

Here we have two points on the line so we have to use the second formula


(ii) m = (y2 - y1)/(x2 - x1)

         m = (3-5) / (1-7)

         m =  -2/(-6)

         m = 1/3  slope of the line

Related Topics





Slope of the line to Analytical Geometry