The equation of the line passing through origin and parallel to the line 3x + 4y + 7 = 0 is:

Given,

⇒ 3x + 4y + 7 = 0

⇒ 4y = -3x - 7

⇒ y = $-\frac{3}{4}x - \frac{7}{4}$

Comparing above equation with y = mx + c, we get :

m = $-\frac{3}{4}$.

By point-slope formula,

Equation of line : y - y₁ = m(x - x₁)

Thus, equation of line parallel to 3x + 4y + 7 = 0 and passing through origin (0, 0) is :

⇒ y - 0 = $-\frac{3}{4}$ (x - 0)

⇒ y = $-\frac{3x}{4}$

⇒ 4y = -3x

⇒ 4y + 3x = 0.

Hence, option 4 is the correct option.