Question 328541
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Calculate the slope of your first line:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ m\ =\ \frac{y_1\ -\ y_2}{x_1\ -\ x_2} ]


where *[tex \Large \left(x_1,y_1\right)] and *[tex \Large \left(x_2,y_2\right)] are the coordinates of the given points.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ m_1\ =\ \frac{-7\ -\ 5}{1\ -\ (-8)} =\ \frac{-4}{3}]


Calculate the slope of your second line:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ m_2\ =\ \frac{6\ -\ b}{3\ -\ (-1)} =\ \frac{6\ -\ b}{4}]


In order for the two lines to be perpendicular, the relationship *[tex \LARGE m_2\ =\ -\frac{1}{m_1}] must hold.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -\frac{1}{m_1}\ =\ -\frac{1}{\frac{-4}{3}}\ =\ \frac{3}{4}]


So set *[tex \LARGE \frac{6\ -\ b}{4}\ =\ \frac{3}{4}]


And just solve for *[tex \LARGE b]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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