For what value of a are the graphs of 6y=−2x+4 and 2y=ax−5 parallel? perpendicular?

a) Parallel when a = -2/3

b) Perpendicular when a = 6

Explanation:

a)  For two parallel lines slopes are equal.

  So, 6y=−2x+4 and 2y=ax−5 parallel if they are slopes equal.

  Slope of 6y=−2x+4, comparing with y = mx + c

     So, m = -2/6 = =-1/3

  For 6y=−2x+4 and 2y=ax−5 to b parallel we have slope of 2y=ax−5 equal to -1/3

   Slope of 2y=ax−5

           m = a/2

    We have a/2 = -1/3

                    a = -2/3

b) For perpendicular lines product of slope is -1.

   So we have

answer: it is 1: 47 pm

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