LINE PASSING THROUGH A POINT AND PARALLEL OR PERPENDICULAR TO THE LINE

Question 1 :

Find the equation of the straight line parallel to the line 3x – y + 7 = 0 and passing through the point (1,-2).

Solution :

Here, the required line is parallel to the given line 3x - y + 7 = 0.Then their slopes will be equal.

m = -3/(-1), m = 3

Equation of the line :

(y - y₁) = m (x - x₁)

(y - (-2)) = 3(x - 1)

y + 2 = 3 x - 3

3x - y - 3 -2 = 0

3x - y - 5 = 0

Question 2 :

Find the equation of the straight line perpendicular to the straight line x – 2y + 3 = 0 and passing through the point (1,-2).

Solution :

Here the required line is perpendicular to the given line x – 2y + 3 = 0

m  =  -1/(-2)

  =  1/2       

slope of the required line = -1/m

  =  -1/(1/2)

  =  -2

Equation of the line

(y - y₁) = m (x - x₁)

(y - (-2)) = -2(x - 1)

y + 2 = -2 x + 2

2x + y + 2 - 2 = 0

2x + y = 0

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