Question

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

Answer 1

Since 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 line
y - y₁ = m(x - x₁)
⇒ y - 4 = `(-3)/(5)(x - 0)`
⇒ 5y - 20 = -3x
⇒ 3x + 5y = 20.