SOLUTION: A line m goes through the point (4,-3) and is perpendicular to the line 3x+2y=9. The point (k,k+3) lies on this perpendicular line m. Find the value of k. Thanks for your help.

Question 945630: A line m goes through the point (4,-3) and is perpendicular to the line 3x+2y=9. The point (k,k+3) lies on this perpendicular line m. Find the value of k. Thanks for your help.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
A line m goes through the point (4,-3) and is perpendicular to the line 3x+2y=9. The point (k,k+3) lies on this perpendicular line m. Find the value of k.
***
3x+2y=9
2y=-3x+9
y=-3/2+9/2
slope:-3/2
slope of perpendicular line=2/3(negative reciprocal)
using coordinates of given points on the perpendicular line:
slope=∆y/∆x=((k+3)-(-3))/(k-4)=2/3
(k+6)/(k-4)=2/3
3k+18=2k-8
k=-26
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