To write the equation of a line that is parallel to the given line \( y = -3x - 2 \), we need to maintain the same slope. The slope of the given line is \(-3\).
To ensure that the new line does not share any points with the original line, we can choose a different y-intercept.
The equation of a line in slope-intercept form is given by:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept. In this case, we need the slope \( m = -3 \) and any y-intercept \( b \) that is different from \(-2\).
Among the options provided, the line \( y = -3x + 8 \) has the same slope of \(-3\) but a different y-intercept (+8). Therefore, it will be parallel and not share any points with the original line.
So, the correct answer is:
y = -3x + 8