The equation of the line can be expressed as

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

To formulate the equation of a line, it is essential to identify two key components: the slope (or gradient) and the y-intercept. The general equation of a line is given by

$y = mx + c,$

where $m$ represents the slope and $c$ denotes the y-intercept. In this scenario, the slope $m$ is $\frac{1}{2}$ and the y-intercept $c$ is $-2$.

The slope indicates the steepness of the line. A slope of $\frac{1}{2}$ signifies that for every $2$ units you move horizontally to the right, the line ascends by $1$ unit vertically. The y-intercept indicates the point at which the line intersects the y-axis; here, the line crosses the y-axis at $-2$.

By substituting the given slope and y-intercept into the general form, we arrive at

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

This equation allows you to calculate the corresponding value of $y$ for any given value of $x$ by multiplying $x$ by $\frac{1}{2}$ and then subtracting $2$. For instance, if we take $x = 4$, we can find $y$ as follows:

$y = \frac{1}{2} \times 4 - 2 = 2 - 2 = 0.$

This equation is particularly useful for graphing the line or determining specific points along it. It is important to remember that the slope and y-intercept are fundamental elements in understanding the behavior of the line.