Discussion
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?
Answer: D
The correct statement is that L4 is perpendicular to L2 and L4 is parallel to L3.
Write each line as \(y = mx + c\) and compare slopes:
- L1: \(2x - 3y = 5\), slope \(2/3\)
- L2: \(3x + 2y = 8\), slope \(-3/2\)
- L3: \(4x - 6y = 5\), slope \(2/3\)
- L4: \(6x - 9y = 6\), slope \(2/3\)
L1, L3 and L4 are parallel (equal slopes, different intercepts), and each is perpendicular to L2 because \((2/3)(-3/2) = -1\). So L4 is perpendicular to L2 and parallel to L3. The other options each call a parallel pair perpendicular, or a perpendicular pair parallel.
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