SOLUTION: for what value of "a" will the two lines x+3y+2=0 and 6x+ay=0 be perpendicular?

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Question 125788: for what value of "a" will the two lines x+3y+2=0 and 6x+ay=0 be perpendicular?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Put each in the slope-intercept form which is y+=+mx+%2B+b
and m is the slope
x+%2B+3y+%2B+2+=+0
3y+=+-x+-+2
y+=+%28-1%2F3%29x+-+2
--------------------
6x+%2B+ay+=+0
ay+=+-6x
y+=+-%286%2Fa%29x
In order to be perpendicular, the slopes of the lines must
have the relation to eachother m%5B1%5D+=+-%281%2Fm%5B2%5D%29 where
m%5B1%5D+=+-%281%2F3%29
m%5B2%5D+=+-%286%2Fa%29
-%281%2F3%29+=+-%281%2F%28-6%2Fa%29%29
-%281%2F3%29+=+a%2F6
a+=+-2 answer
check the answer
The equations would be
(1) y+=+%28-1%2F3%29x+-+2
(2) y+=+-%286%2F%28-2%29%29x
(2) y+=+3x
m%5B1%5D+=+-%281%2Fm%5B2%5D%29
-%281%2F3%29+=+-%281%2F3%29
OK