Answer to Question #294746 in Analytic Geometry for bookaddict

Question #294746

Find the equation of the line which is perpendicular to 4𝑦=5π‘₯βˆ’8 and passing through (2,3).


1
Expert's answer
2022-02-07T17:47:56-0500
4𝑦=5π‘₯βˆ’8=>y=54xβˆ’24𝑦=5π‘₯βˆ’8=>y=\dfrac{5}{4}x-2

slope1=m1=54slope_1=m_1=\dfrac{5}{4}

If two lines with slopes m1m_1 and m2m_2 are perpendicular then m1m2=βˆ’1.m_1m_2=-1.

Then 54m2=βˆ’1.\dfrac{5}{4}m_2=-1.


slope2=m2=βˆ’45slope_2=m_2=-\dfrac{4}{5}

The equation of the second line is


y=βˆ’45x+by=-\dfrac{4}{5}x+b

This line passes through the point (2,3)(2, 3)


3=βˆ’45(2)+b=>b=y=235x3=-\dfrac{4}{5}(2)+b=>b=y=\dfrac{23}{5}x

The equation of the line which is perpendicular to 4𝑦=5π‘₯βˆ’84𝑦=5π‘₯βˆ’8 and passing through (2,3)(2,3) is


y=βˆ’45x+235y=-\dfrac{4}{5}x+\dfrac{23}{5}

Or


5y=βˆ’4x+235y=-4x+23

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