Question

Find equation of the line parallel to the line 3x – 4y + 2 = 0 and passing through the point (–2, 3).

Answer 1

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