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:



Add -3x+5 to both sides:



Divide every term by -2





So comparing that to y = mx+b
the slope = 

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Now we do the second one:

kx-6y+1=0




Add -kx-1 to both sides:



Divide every term by -6





So comparing that to y = mx+b
the slope = 

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



Cross-multiply:

 2k = 18

  k = 9

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







Multiply both sides by 4

k = -4

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Edwin