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Let P and Q be constants. The graphs of the lines x + 5y = 7 and 16x + Py = Q are perpendicular and intersect at the point (8,3). Enter the ordered pair (P,Q).

 Jan 13, 2021
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The point   8, 3    is not on the line  x + 5y = 7

     the point    -8, 3     IS on the line

         plug into the second equation

                 16(-8)  + p(3) = Q

                   -128 + 3p = q           slope has to be 5 to be perpindicular  (the slope of the first line is  -1/5)

                       16x + py = q

                                  py = - 16x +q        so    -16/p = 5    p = -16/5

                     -128 - 16/5 (3) = q = -640/5 - 48/5 = -688/5 =Q=........

  p

 Jan 13, 2021

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