The slope of two lines are 5/6 and 2/p. determine the value of p that will make the lines
2 answers:
Parallel: the lines have = slopes. We thus need 5/6 to equal 2/p. then 5p must equal 12, and p = 12/5. (answer)
Check: Is 5/6 = 2 / (12/5)? YES
Perp.: The lines have slopes that are negative reciprocals of one another.
Then -6/5 = 2/p, or
-6 2
---- = ----
5 p Thus, -6p = 10, and p = -5/3 (answer)
A) In order to be parallel, the slopes must be the same. To find p, set the slopes equal to each other:
5/6 = 2/p
Cross multiply:
12 = 5p
p = 12/5
B) In order to be perpendicular, the slopes must be opposite reciprocals. So if one line's slope is 5/6, the other line's slope must be -6/5:
-6/5 = 2/p
10 = -6p
p = 10/-6
Reduced, the answer is p = -5/3.
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