If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then the…
2019
If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then the value of k is:
- A.
−5/4
- B.
3/2
- C.
15/4
- D.
2/5
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Correct answer: C
Method: For two lines in the form ax + by + c = 0, the slope is -a/b. Set the slopes equal to make the lines parallel.
First line: 3x + 2ky = 2 can be written 3x + 2ky - 2 = 0, so its slope is -3/(2k).
Second line: 2x + 5y + 1 = 0 has slope -2/5.
Equate the slopes: -3/(2k) = -2/5, which gives 3/(2k) = 2/5.
Solve: cross-multiplying gives 15 = 4k, so k = 15/4.
Answer: k = 15/4.
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