To find the equation of a line that is perpendicular to the line \( y = -3x + 5 \), we need to determine the slope of the perpendicular line.
The slope of the given line \( y = -3x + 5 \) is \(-3\). The slope of a line that is perpendicular to another line is the negative reciprocal of the original line's slope.
The negative reciprocal of \(-3\) is:
\[ \frac{1}{3} \]
Now, we can look for a line with this slope. The correct option should have a slope of \(\frac{1}{3}\).
Among the provided options, the one that matches this condition is:
- \(y = \frac{1}{3}x + 9\)
So, the equation of the line perpendicular to \(y = -3x + 5\) is:
\[ y = \frac{1}{3}x + 9 \]