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Find the value of $a$ such that the lines with equations $y = 2x + 13$ and $6y + ax = 6 + 5y - 3x$ are perpendicular.

 Aug 14, 2023
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y = 2x + 13      the slope  = 2

 

The second line will be perp  when   the slope =  -1/2.....so.....

 

6y + ax = 6 + 5y - 3x          simplify as

 

y = -ax - 3x + 6

 

y = - (a + 3) + 6             the slope =  - (a + 3).....set this = -1/2

 

-1/2 = - (a + 3)

 

1/2 = a + 3

 

1/2 - 3  = a

 

1/2 - 6/2  =  a

 

-5/2 =  a

 

cool cool cool

 Aug 14, 2023
edited by CPhill  Aug 14, 2023

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