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 - y_{1} = m(x - x_{1})
(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 - y_{1} = m(x - x_{1})
(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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