Question

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

Answer 1

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)

Answer 2

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.