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Consider the following equations of straight lines: Line L1: 2x - 3y = 5 Line L2: 3x + 2y = 8 Line L3: 4x - 6y = 5 Line L4: 6x - 9y = 6 Which one among the following is the correct statement?

1. L1 is parallel to L2 and L1 is perpendicular to L3
2. L2 is parallel to L4 and L2 is perpendicular to L1
3. L3 is perpendicular to L4 and L3 is parallel to L2
4. L4 is perpendicular to L2 and L4 is parallel to L3

Correct answer: L4 is perpendicular to L2 and L4 is parallel to L3

Solution

Line L4 is perpendicular to L2 because the product of their slopes equals -1, indicating they intersect at a right angle. Additionally, L4 is parallel to L3 since both lines have the same slope, confirming they never intersect.

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