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Determine if the given pairs of lines are parallel.

a. \( L_1: (-1, 1), (1, 7); \quad L_2: (-2, -5), (1, 4) \)

b. \( L_1: (-2, -5), (1, 4); \quad L_2: (-1, 7), (2, 1) \)

c. \( L_1: (-2, 2), (4, -1); \quad L_2: (4, -5), (2, -4) \)

d. \( L_1: (2, -3), (1, -1); \quad L_2: (-1, 3), (2, -3) \)

Answer :

Final answer:

We can determine if the pairs of lines are parallel by calculating the slopes of the lines and comparing them. If the slopes are the same, the lines are parallel.

Explanation:

To determine if the given pairs of lines are parallel or not, we would need to calculate the slopes of these lines. Two lines are parallel if they have the same slope. The formula for the slope (m) of a line between two points (x1, y1) and (x2, y2) is m = (y2 - y1) / (x2 - x1).

  • For L1: (-1, 1), (1, 7), the slope m1 = (7 - 1) / (1 - (-1)) = 3

  • For L2: (-2. -5), (1, 4), the slope m2 = (4 - (-5)) / (1 - (-2)) = 3

Using similar calculations for the rest of the lines, we can just compare the slopes. If they are equal, the lines are parallel. If not, they are not parallel.

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