FINDING EQUATION OF PARALLEL LINE

Example 1 :

Find an equation of the line through P(1, -2) that is parallel to the line L with equation 3x - 2y  =  1.

Solution :

2y  =  3x - 1

y  =  (3/2)x - (1/2)

Slope of the given line is 3/2. If two lines are parallel, then slopes will be equal.

The required line is having the slope 3/2 and passing through the point (1, -2).

Equation of the line :

y - y₁  =  m(x - x₁)

(y + 2)  =  (3/2) (x - 1)

2(y + 2)  =  3(x - 1)

2y + 4  =  3x - 3

3x - 2y - 3 - 4  =  0

3x - 2y - 7  =  0

Hence the equation of the required line is 3x - 2y - 7  =  0.

Example 2 :

Find an equation of the line through P(3, 1) that is parallel to the line L with equation 2x + 3y  =  12

Solution :

3y  =  -2x + 12

y  =  (-2/3)x + (12/3)

Slope of the given line is -2/3. If two lines are parallel, then slopes will be equal.

The required line is having the slope -2/3 and passing through the point (3, 1).

Equation of the line :

y - y₁  =  m(x - x₁)

(y - 1)  =  (-2/3) (x - 3)

3(y - 1)  =  -2(x - 3)

3y - 3  =  -2x + 6

2x + 3y - 3 - 6  =  0

2x + 3y - 9  =  0

Hence the equation of the required line is 2x + 3y - 9 = 0.

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