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

3x - 4y= 7

8x + Ay = B

 

The slope of the first line is 4/3

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

 

So  we can write the second line as

 

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

 

So......this implies that   

 

(-8/A)  = -3/4

 

A /-8  =  -4/3

 

A = 32/3 

 

So we have that

 

2 =  (-3/4) (5) + B/(32/3)

 

B = 184/3

 

So  A + B =   32/3 + 184/3  =  72