SOLUTION: If the line is perpendicular to 3x-4y=2 and B=2 then solve for A. Keeping in mind the equation Ax+By=13

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Question 159308: If the line is perpendicular to 3x-4y=2 and B=2 then solve for A. Keeping in mind the equation Ax+By=13
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let's find the slope of the first line.
Convert to slope-intercept form , y=mx%2Bb
3x-4y=2
-4y=2-3x
y=%283x-2%29%2F4
y=%283%2F4%29x-1%2F2
The slope of the first line is m%5B1%5D=3%2F4
Convert the second equation to slope-intercept form , y=mx%2Bb
Ax%2BBy=13
By=13-Ax
y=13%2FB-%28A%2FB%29x
But you know B=2
y=13%2F2-%28A%2F2%29x
The slope of the second line is
m%5B2%5D=-%28A%2F2%29
Perpendicular line have the property that their slopes are negative reciprocals of each other.
m%5B1%5Dm%5B2%5D=-1
%283%2F4%29%28-A%2F2%29=-1
A=8%2F3
We can plot both lines to check the answer and perpendicularity.
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