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Question
Find equation of the line parallel to the line 3x – 4y + 2 = 0 and passing through the point (–2, 3).
Solution
3x – 4y + 2 = 0
or 4y = 3x + 2
∴ y = `3/4 "x" + 2/4`
∴ Slope of the line = `3/4`
Equation of the line passing through the given point (−2, 3) and slope m = `3/4`
y – y1 = m(x – x1)
y – 3 = `3/4 ("x" + 2)`
or 4y – 12 = 3x + 6
or 3x – 4y + 18 = 0
Second method: Any line parallel to ax + by + c = 0 can be written as ax + by + k = 0.
∴ The line parallel to 3x – 4y + 2 = 0 is 3x – 4y + k = 0
It passes through (−2, 3).
∴ 3 x (−2) – 4 x 3 + k = 0 or k = 18
Equation of required parallel line: 3x – 4y + 18 = 0
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