FINDING SLOPE OF THE LINE WHEN ANGLE OF INCLINATION IS GIVEN

Formula to find slope when angle of inclination is given :

m  =  tan θ

Problem 1 :

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

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

Solution :

(i)  Slope  =  1

m = tan θ

tan θ  =  1

θ  =  45

 (ii) √3

m = tan θ

tan θ  =  √3

θ  =  60

(iii) 0

m = tan θ

tan θ  =  0

θ  =  0

Problem 2 :

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

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

(i) θ  =  30°  

m = tan θ

m  =  tan 30

m  =  1/√3

(ii) θ  =  60°  

m = tan θ

m  =  tan 60

m  =  √3

(iii) 90°

m = tan θ

m  =  tan 90

m  =  undefined

Problem 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

Problem 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  =  1

tan θ  =  1

θ  =  45

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

m  =  (0 - 3)/(0 - 3)

m  =  1

tan θ  =  1

θ  =  45

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

m  =  (-b - b)/(-a - a)

m  =  (-2b)/(-2a)

tan θ  =  b/a

θ  =  tan-1 (b/a)

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