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?
+128448 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
