To determine which of the lines are parallel, we need to calculate the slopes of each line. Two lines are parallel if they have the same slope.

The slope formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$

Line a:

Points: (-1, -2) and (1, 0) $m_a = \frac{0 - (-2)}{1 - (-1)} = \frac{0 + 2}{1 + 1} = \frac{2}{2} = 1$

Line b:

Points: (4, 2) and (2, -2) $m_b = \frac{-2 - 2}{2 - 4} = \frac{-4}{-2} = 2$

Line c:

Points: (0, 2) and (-1, 1) $m_c = \frac{1 - 2}{-1 - 0} = \frac{-1}{-1} = 1$

Conclusion:

• Line a has a slope of 1.
• Line b has a slope of 2.
• Line c has a slope of 1.

Since line a and line c both have a slope of 1, lines a and c are parallel.

The correct answer is: lines a and c; they have the same slope.

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

Here are 5 related questions you could explore:

1. How do you calculate the equation of a line from two points?
2. Can two lines with the same slope ever be non-parallel?
3. What is the slope of a vertical line?
4. How do you find the point of intersection of two non-parallel lines?
5. How do you determine if two lines are perpendicular based on their slopes?

Tip: For any two lines, if their slopes are equal, they are parallel. If the product of their slopes is -1, they are perpendicular!