SOLUTION: Here is my question: If the lines 3x + Ky = 2 and 6x - 5y - 1 = 0 are parallel, what is the value of K? I figured out that the slope of 6x - 5y - 1 = 0 is 6/5 and know that

Algebra ->  Algebra  -> Linear-equations -> SOLUTION: Here is my question: If the lines 3x + Ky = 2 and 6x - 5y - 1 = 0 are parallel, what is the value of K? I figured out that the slope of 6x - 5y - 1 = 0 is 6/5 and know that       Log On

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Question 18388: Here is my question:
If the lines 3x + Ky = 2 and 6x - 5y - 1 = 0 are parallel, what is the value of K?
I figured out that the slope of 6x - 5y - 1 = 0 is 6/5 and know that the slope is the same for the other equation since they are parallel, but I don't know how to apply it to the 1st equation.
Please Help!
Thanks!
Sandy
Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
First, you need to write both equations in the slope-intercept form: y+=+mx+%2B+b
1) 3x+%2B+Ky+=+2 Subtract 3x from both sides.
Ky+=+-3x+%2B+2 Divide both sides by K
+y+=+%28-3%2FK%29x+%2B+2%2FK The slope is: m+=+%28-3%2FK%29
2) 6x+-+5y+-+1+=+0 Add 5y to both sides.
6x+-+1+=+5y Divide both sides by 5.
y+=+%286%2F5%29x+-+1%2F5 The slope is: m+=+6%2F5
Since the lines are parallel, the slopes must be equal, as you have correctly noted.
%28-3%2FK%29+=+6%2F5 Solve for K. Multiply both sides by K.
-3+=+6K%2F5 Multiply both sides by 5.
-15+=+6K Divide both sides by 6.
%28-15%29%2F6+=+K Simplify.
K+=+%28-5%2F2%29