$A$ 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 $A+B?$

Gordn Jul 26, 2022

#1**0 **

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

Guest Jul 26, 2022