To determine whether lines $AB$ and $CD$ are parallel, perpendicular, or neither, we need to compare their slopes.

Step 1: Calculate the slope of line $AB$.

The slope formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ For $A(4, 2)$ and $B(-3, 1)$: $m_{AB} = \frac{1 - 2}{-3 - 4} = \frac{-1}{-7} = \frac{1}{7}$

Step 2: Calculate the slope of line $CD$.

For $C(-6, 0)$ and $D(1, 1)$: $m_{CD} = \frac{1 - 0}{1 - (-6)} = \frac{1}{7}$

Step 3: Compare the slopes.

• If the slopes are equal, the lines are parallel.
• If the product of the slopes is $-1$, the lines are perpendicular.

Since $m_{AB} = \frac{1}{7}$ and $m_{CD} = \frac{1}{7}$, the lines are parallel.

Answer: A. Parallel

Would you like more details on the solution or have any questions?

Here are 5 related questions you can explore:

1. How can you determine if two lines are perpendicular from their slopes?
2. What is the geometric interpretation of parallel lines?
3. What does it mean for lines to be skew in three-dimensional space?
4. How would you calculate the distance between two parallel lines?
5. What happens when the slope of one line is undefined (vertical line)?

Tip: For lines to be perpendicular, the product of their slopes must always equal $-1$.