# Answer to Question #30158 in Analytic Geometry for jane

Question #30158

determine b so that the line 2x+b+2=0 is perpendicular to the line 3x+2y-7+0

Expert's answer

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.

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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