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The equation of line m is 3x + 4y = 12.  The line whose equation is 3x + 4y = k is 2 units from m.  Find the two possible values of k.

 Dec 6, 2019
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3x  +  4y  =  12

 

The  x intercept  of this line  is   ( 0, 3)

 

Using   the  formula   for the distance  from  a point to a line we have that

 

l  3 ( 0)  + 4(3)   -  k  l

__________________   =      2

  sqrt ( 3^2 + 4^2)

 

 

1  3(0)   + 4(3)  - k  l

__________________  =      2         ......   multiply both sides by 5  and simplify

             5

 

 

l  12  - k l    =   10            we have two equations

 

12 - k  =  10              12  - k  =  -10

 

k   =  2        or       k  = 22

 

Here's a graph  :   https://www.desmos.com/calculator/vj8dt6sx7z

 

 

cool cool cool

 Dec 6, 2019

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