To write the equation of a line that is parallel to the line \( y = -3x - 2 \), it needs to have the same slope, which is \(-3\). However, to ensure that the line does not share any points with the original line, it must have a different y-intercept.
Among the options provided, we need to check which one has the same slope of \(-3\) but a different y-intercept:
- \( y = -3x + 8 \) (same slope, different intercept)
- \( y = 3x + 8 \) (different slope)
- \( y = 3x - 2 \) (different slope)
- \( y = -3x - 2 \) (same slope and same intercept)
The only option that is parallel (same slope \(-3\)) and does not share any points (different y-intercept) is:
\( y = -3x + 8 \).