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 Apr 19, 2019

#1**+1 **

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?

Slope of first line = 3/4

Slope of second line = -4/3

Rearrange the second equation

Ay = -8x+ B

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

Which implies that -8/A = -4/3 so 24 = 4A ⇒ A = 6

And since (5,2) is on the both lines...then

(6) 2 = -8(5) + B

12 = -40 + B

52 = B

A + B = 6 + 52 = 58

Here's a graph : https://www.desmos.com/calculator/4q0eh6wjme

CPhill Apr 19, 2019