Given vectors $\vec{a} = (1, x)$ and $\vec{b} = (2, -4)$, find the value of $x$ if $\vec{a}$ is parallel to $\vec{b}$.

1. Problem Description

Given vectors $\vec{a} = (1, x)$ and $\vec{b} = (2, -4)$, find the value of $x$ if $\vec{a}$ is parallel to $\vec{b}$.

2. Solution Steps

If two vectors $\vec{a} = (a_1, a_2)$ and $\vec{b} = (b_1, b_2)$ are parallel, then their components are proportional, i.e.,

$\frac{a_1}{b_1} = \frac{a_2}{b_2}$.

In our case, $\vec{a} = (1, x)$ and $\vec{b} = (2, -4)$. Therefore,

$\frac{1}{2} = \frac{x}{-4}$.

To solve for $x$, we can multiply both sides of the equation by $-4$:

$x = \frac{1}{2} \times (-4)$

$x = -2$

3. Final Answer

The value of $x$ is $-2$. So the correct option is A.