Question 882302
<pre>
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}}}{{{""=""}}}{{{"0"}}}

Add -3x+5 to both sides:

{{{-2y}}}{{{""=""}}}{{{-3x+5}}}

Divide every term by -2

{{{(-2y)/(-2)}}}{{{""=""}}}{{{expr((-3)/(-2))x+5/(-3)}}}

{{{y}}}{{{""=""}}}{{{expr((3)/(2))x-5/(3)}}}

So comparing that to y = mx+b
the slope = {{{3/2}}}

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Now we do the second one:

kx-6y+1=0


{{{kx-6y+1}}}{{{""=""}}}{{{"0"}}}

Add -kx-1 to both sides:

{{{-6y}}}{{{""=""}}}{{{-kx-1}}}

Divide every term by -6

{{{(-6y)/(-6)}}}{{{""=""}}}{{{expr((-k)/(-6))x-1/(-6)}}}

{{{y}}}{{{""=""}}}{{{expr((k)/(6))x+1/(6)}}}

So comparing that to y = mx+b
the slope = {{{k/6}}}

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

{{{k/6}}}{{{""=""}}}{{{3/2}}}

Cross-multiply:

 2k = 18

  k = 9

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

{{{(k/6)(3/2)}}}{{{""=""}}}{{{-1}}}

{{{3k/12}}}{{{""=""}}}{{{-1}}}

{{{k/4}}}{{{""=""}}}{{{-1}}}

Multiply both sides by 4

k = -4

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Edwin</pre>