To write the equation of a line that is parallel to \( y = -3x - 2 \), we need to keep the same slope, which is \(-3\), but it must have a different y-intercept to ensure it does not share any points with the original line.
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. Since we want the slope to remain \(-3\), we can write the equation as:
\[ y = -3x + b \]
Now, to make sure the new line does not share any points with the original line, we need to choose a different y-intercept \( b \) from the one in the original equation, which is \(-2\).
Looking at the options you provided, we can choose the equation \( y = -3x + 8 \), where the slope is \(-3\) and the y-intercept is \(8\), which is different from \(-2\).
Thus, the correct answer is:
y = -3x + 8