Consider the line $3 x-9 y=-2$ What is the slope of a line parallel to this line? What is the slope of a line perpendicular to this line? Slope of a parallel line: Slope of a perpendicular line:

Step 1 ：Given the line equation in the form $ax + by = c$, where $a = 3$ and $b = -9$.

Step 2 ：The slope of a line in this form is given by $-a/b$. So, the slope of the given line is $-3/-9 = 1/3$.

Step 3 ：A line parallel to the given line will have the same slope. Therefore, the slope of a line parallel to the given line is also $1/3$.

Step 4 ：A line perpendicular to the given line will have a slope that is the negative reciprocal of the given line's slope. Therefore, the slope of a line perpendicular to the given line is $-1/(1/3) = -3$.

Step 5 ：Final Answer: The slope of a line parallel to the given line is \(\boxed{\frac{1}{3}}\) and the slope of a line perpendicular to the given line is \(\boxed{-3}\).