SOLUTION: A line has the equation 2x+5y=7. Another line passes through (3,6) and (k,9). What value for "k" will make the lines parallel?

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Question 419919: A line has the equation 2x+5y=7. Another line passes through (3,6) and (k,9). What value for "k" will make the lines parallel?
Found 2 solutions by josmiceli, nerdybill:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Both equations need to be in the form +y+=+mx+%2B+b
where m is the slope
2x+%2B+5y+=+7
+5y+=+-2x+%2B+7
+y+=+%28-2%2F5%29%2Ax+%2B+7%2F5+
Any line parallel to this one must have m+=+-2%2F5
--------------
(3,6) , (k,9)
The formula for line through 2 points is:
+%28y+-+6%29+%2F+%28x+-+3%29+=+%289+-+6%29+%2F+%28k+-+3%29+
++%28y+-+6%29+%2F+%28x+-+3%29+=+3+%2F+%28k+-+3%29+
+%28y+-+6%29%2A%28k+-+3%29+=+3%2A%28x+-+3%29+
+k%2Ay+-+6k+-+3y+%2B+18+=+3x+-+9+
+%28k+-+3%29%2Ay+=+3x+-+9+-+18+%2B+6k+
+%28k+-+3%29%2Ay+=+3x+%2B+6k+-+27+
+y+=+%283%2F%28k+-+3%29%29%2Ax+%2B+%286k+-+27%29%2F%28k+-+3%29+
--------------
+-2%2F5+=+3%2F%28k+-+3%29+
-2%2A%28k+-+3%29+=+15+
-2k+%2B+6+=+15
-2k+=+9
k+=+-9%2F2 answer
check answer:

+y+=+%283%2F%28-15%2F2%29%29%2Ax+%2B+%28-27+-+27%29%2F%28-15%2F2%29+
+y+=+%28-2%2F5%29%2Ax+%2B+%28-27+-+27%29%2F%28-15%2F2%29+
OK

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
A line has the equation 2x+5y=7. Another line passes through (3,6) and (k,9). What value for "k" will make the lines parallel?
.
first, find slope of:
2x+5y=7
5y= -2x+7
y= (-2/5)x+7/5
slope then, is -2/5
.
a parallel line must have the same slope so applying:
slope = (y2 - y1)/(x2 - x1)
.
-2/5 = (9 - 6)/(k - 3)
-2/5 = 3/(k - 3)
cross multiplying:
-2(k-3) = 15
-2k + 6 = 15
-2k = 9
k = -9/2