SOLUTION: Please can someone help me, I tried lots of times to solve it but I couldn't. So the queston is: Find the value of k for which the lines 3x-2y-5=0 and kx-6y+1=0 are: a) paralle

Algebra ->  Linear-equations -> SOLUTION: Please can someone help me, I tried lots of times to solve it but I couldn't. So the queston is: Find the value of k for which the lines 3x-2y-5=0 and kx-6y+1=0 are: a) paralle      Log On


   

Question 882302: Please can someone help me, I tried lots of times to solve it but I couldn't. So the queston is: Find the value of k for which the lines 3x-2y-5=0 and kx-6y+1=0 are:
a) parallel
b)perpendicular
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
3x-2y-5=0 and kx-6y+1=0
 
We need the slope of each

Get them both in slope-y-intercept form y=mx+b

Start with the first one:

3x-2y-5%22%22=%22%22%220%22

Add -3x+5 to both sides:

-2y%22%22=%22%22-3x%2B5

Divide every term by -2

%28-2y%29%2F%28-2%29%22%22=%22%22expr%28%28-3%29%2F%28-2%29%29x%2B5%2F%28-3%29

y%22%22=%22%22expr%28%283%29%2F%282%29%29x-5%2F%283%29

So comparing that to y = mx+b
the slope = 3%2F2

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Now we do the second one:

kx-6y+1=0


kx-6y%2B1%22%22=%22%22%220%22

Add -kx-1 to both sides:

-6y%22%22=%22%22-kx-1

Divide every term by -6

%28-6y%29%2F%28-6%29%22%22=%22%22expr%28%28-k%29%2F%28-6%29%29x-1%2F%28-6%29

y%22%22=%22%22expr%28%28k%29%2F%286%29%29x%2B1%2F%286%29

So comparing that to y = mx+b
the slope = k%2F6

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(a) For the two lines to be parallel the slopes must be equal:

k%2F6%22%22=%22%223%2F2

Cross-multiply:

 2k = 18

  k = 9

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(b) For the two lines to be parallel their product must be -1

%28k%2F6%29%283%2F2%29%22%22=%22%22-1

3k%2F12%22%22=%22%22-1

k%2F4%22%22=%22%22-1

Multiply both sides by 4

k = -4

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Edwin