$A$ 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 $A+B?$
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 !!!