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 $A$ and $B$ are constants such that the graphs of the lines $3x - 4y  = 7$ and $8x + Ay = B$ are perpendicular and intersect at $(5,2).$ What is $A+B?$

Guest Nov 19, 2017
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3x - 4y= 7

8x + Ay = B

 

The slope of the first line is 3/4

So....the slope of the second line will be  -4/3 

 

So  we can write the second line as

 

Ay  =  -8x + B  ⇒  y  =  (-8/A)x + B/A

 

So......this implies that   

 

(-8/A)  = -4/3

 

A /-8  =  -3/4

 

A = 24/ 4   = 6

 

So we have that

 

2 =  (-4/3) (5) + B/6

 

2 = -20/3 + B/6

 

12 = -40 + B

 

52  = B

 

So  A + B =    6 + 52  =  58

 

 

Here's a graph : https://www.desmos.com/calculator/pgimsvymds

 

Thanks to hectictar for spotting my earlier mistake ....she always keeps me straight  !!!

 

 

 

 

 

 

cool cool cool

CPhill  Nov 19, 2017
edited by CPhill  Nov 19, 2017

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