Find the $x$ and $y$ intercepts of the line $2x + \sqrt{3}y + 1 = 0$.

1. Problem Description

Find the $x$ and $y$ intercepts of the line $2x + \sqrt{3}y + 1 = 0$.

2. Solution Steps

To find the $x$-intercept, set $y=0$ and solve for $x$.

$2x + \sqrt{3}(0) + 1 = 0$

$2x + 1 = 0$

$2x = -1$

$x = -\frac{1}{2}$

To find the $y$-intercept, set $x=0$ and solve for $y$.

$2(0) + \sqrt{3}y + 1 = 0$

$\sqrt{3}y + 1 = 0$

$\sqrt{3}y = -1$

$y = -\frac{1}{\sqrt{3}}$

$y = -\frac{\sqrt{3}}{3}$

The x and y intercepts are $-\frac{1}{2}$ and $-\frac{\sqrt{3}}{3}$ respectively.

3. Final Answer

B. $-\frac{1}{2}; -\frac{\sqrt{3}}{3}$