Question

Find the equation of the line passing through (0, 4) and parallel to the line 3x + 5y + 15 = 0.

Answer 1

Since the line is parallel to,

3x + 5y + 15 = 0

5y = −3x − 15

y = `(-3)/(5) x - 3`

∴ m₁ = `(-3)/(5)`

m₁ = m₂  ...(∵ lines are parallel)

∴ m₂ = `(-3)/(5)`

and passing point = (0, 4)

Equation of a line,

y − y₁ = m(x − x₁)

⇒ y − 4 = `(-3)/(5)(x - 0)`

⇒ 5y − 20 = −3x

⇒ 3x + 5y − 20 = 0 or 3x + 5y = 20