determine b so that the line 2x+b+2=0 is perpendicular to the line 3x+2y-7+0
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Expert's answer
2013-05-15T10:29:27-0400
We have first line 2x+by+2=0. Then we can find y from this equality, and write y as linear function of x. Thus first line is y=(-2/b)x-2/b.
Similarly, with second line we have: second line is y=(-3/2)x+3.5.
If equation of a line is written as y=mx+h, then its slope is coefficient m. Theorem tells: Lines are perpendicular iff product of their slopes is equal -1.
First slope is m1=-2/b. Second one is m2=-3/2.
So, they will be perpendicular if (-2/b) * (-3/2) = - 1 Then simplifying we obtain: 3 / b = - 1. b = -3 - is the answer.
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