$A$ 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

#1**+2 **

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 !!!

CPhill
Nov 19, 2017