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# Find distance between x and y intercept

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\$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
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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
edited by CPhill  Nov 19, 2017

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