# FINDING SLOPE OF THE LINE WHEN ANGLE OF INCLINATION IS GIVEN

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

Here we are going to see some practice questions on finding slope of the line when angle of inclination is given.

Formula to find slope when angle of inclination is given :

m = tan θ

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

Question 1 :

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

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

Solution :

 (i)  Slope  =  1m = tan θtan θ  =  1θ  =  45 (ii) √3m = tan θtan θ  =  √3θ  =  60

(iii) 0

m = tan θ

tan θ  =  0

θ  =  0

Question 2 :

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

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

 (i) θ  =  30°  m = tan θm  =  tan 30m  =  1/√3 (ii) θ  =  60°  m = tan θm  =  tan 60m  =  √3

(iii) 90°

m = tan θ

m  =  tan 90

m  =  undefined

Question 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

Question 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 :

 (i) (1, 2) and (2 , 3)m  =  (3 - 2)/(2 - 1)m  =  1tan θ  =  1θ  =  45 (ii) (3 , 3) and (0 , 0)m  =  (0 - 3)/(0 - 3)m  =  1tan θ  =  1θ  =  45

(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, finding slope of the line when angle of inclination is given.

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