FINDING SLOPE OF THE LINE WHEN ANGLE OF INCLINATION IS GIVEN

Finding Slope of the Line When Angle of Inclination is Given :

In this section, you will learn how to find the slope of a line when its angle of inclination is given. 

Finding Slope of the Line When Angle of Inclination is Given - Examples

Example 1 :

Find the angle of inclination of the straight line whose slope is

(i) 1          (ii) √3            (iii) 0

Solution :

(iii) 0

m = tan θ

tan θ  =  0

θ  =  0

Example 2 :

Find the slope of the straight line whose angle of inclination is

(i) 30°       (ii) 60°         (iii) 90°

(iii) 90°

m = tan θ

m  =  tan 90

m  =  undefined

Example 3 :

Find the slope of the straight line passing through the points

(i) (3 , -2) and (7 , 2)

(ii) (2 , -4) and origin

(iii) (1 + √3 , 2) and (3 + √3 , 4)

Solution :

(i)  m  =  (y₂ - y₁)/(x₂ - x₁)

m  =  (2 + 2)/(7 - 3)

m  =  4/4

m  =  1

Hence the slope passing through the given points is 1.

(ii)  m  =  (y₂ - y₁)/(x₂ - x₁)

(2 , -4) and (0, 0)

m  =  (0 + 4)/(0 - 2)

m  =  4/(-2)

m  =  -2

(iii) (1 + √3 , 2) and (3 + √3 , 4)

m  =  (y₂ - y₁)/(x₂ - x₁)

m  =  (4 - 2)/[(3 + √3) - (1 + √3)]

m  =  2/2

m  =  1

Example 4 :

Find the angle of inclination of the line passing through the points

(i) (1, 2) and (2 , 3)

(ii) (3 , 3) and (0 , 0)

(iii) (a , b) and (-a , -b)

Solution :

(iii) (a , b) and (-a , -b)

m  =  (-b - b)/(-a - a)

m  =  (-2b)/(-2a)

tan θ  =  b/a

θ  =  tan^-1 (b/a)

After having gone through the stuff given above, we hope that the students would have understood how to find the slope of a line when its angle of inclination is given.

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