SOLUTION: Determine the bisector of the obtuse angle between the line 2x-3y=2 and x+y=6. Sketch the graph.

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Question 641198: Determine the bisector of the obtuse angle between the line 2x-3y=2 and x+y=6. Sketch the graph.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

+graph%28+600%2C600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%2B6%2C+2x%2F3-2%2F3%29+
The slope of the bisecting line is NOT the average of the slopes of the two given lines.
We need to find a point on the line of intersection and its slope. First find the point of intersection of the lines:
2x+-+3y+=+2
x+%2B+y+=+6
The point of intersection is P(4,+2).
Find the slopes of the given lines.
m1+=+tan%28alpha%29+=+2%2F3
m2+=+tan%28beta%29+=+-1
Note that for the first line alpha%3C+45°.
Note that for the second line beta+=+135°.
beta+-+alpha+%3E+90°
Therefore for the bisecting line of the obtuse angle:
m+=+tan%28%28alpha+%2B+beta%29%2F2%29
So the bisector of the obtuse angle will be near+vertical.
The equation of the line will be:
y+-+2+=+m%28x+-4%29