Question

The slope of two lines are 5/6 and 2/p. determine the value of p that will make the lines

A)parallel
B) perpendicular

Answer 1

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.

Answer 2

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)