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Let P and Q be constants. The graphs of the lines x - 5y = 7 and 15x + Py = Q are perpendicular and intersect at the point (8,3)  Enter the ordered pair (P,Q).

 Jan 17, 2021
 #1
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This question (or similar) was posted the other day....with the same mistake....   8,3 is not on the line    x - 5y = 7      

 Jan 17, 2021
 #2
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....is that supposed to be    x - 5y = - 7 ??

Guest Jan 17, 2021
 #4
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Assuming   x-5y = -7

Slope of first line =   1/5     perpindicular = -5

   Py = -15x + Q

     y = - 15/P  + Q /P       -15/P = -5     so P = 3

 

15(8) + 3(3) = Q      Q = 129

Guest Jan 17, 2021
 #3
avatar+116126 
+1

Maybe you meant   x - 5y  =  -7     ???

 

If so....rearrange as

 

-5y  =  -x - 7          divide  both sides by   -5

y = (1/5) + 7/5

 

The slope of this line   =   1/5

A perpendicular line has the slope   -  5

 

Rearrange     15x + Py   = Q     as

 

Py   =   -15x  +   Q         

 

y  =   (-15/P)x  +   Q/P     

 

To  have a slope of  -5,  P  must  be  =  3 

 

So   we have     

 

y =  -5x  +  Q/3

 

And since  (8,3)   is on this line we have that

 

3 = -5(8)  + Q/3

 

3   = -40  +  Q/3

 

43  =  Q/3          multiply through by 3

 

129 =   Q

 

So   (P,Q)   =   (3, 129)

  

 

 

cool cool cool

 Jan 17, 2021

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