The equation of a straight line whose inclination with x-axis is 30° and whose y-intercept is –4, is:

1. $\sqrt{3}x - y - 4\sqrt{3} = 0$

2. $x + \sqrt{3}y - 4\sqrt{3} = 0$

3. $x - \sqrt{3}y - 4\sqrt{3} = 0$

4. $\sqrt{3}x + y - 4\sqrt{3} = 0$

The slope m is determined by the inclination θ = 30°.

m = tan θ

m = tan 30°

m = $\dfrac{1}{\sqrt3}$

Slope-intercept form:

y = mx + c

$\Rightarrow y = \dfrac{1}{\sqrt3}x - 4 \\[1em] \Rightarrow \sqrt3y = x - 4\sqrt3 \\[1em] \Rightarrow x - \sqrt3y - 4\sqrt3 = 0.$

Hence, option 3 is the correct option.