Write an equation of the line passing through point P (2,3) that is perpendicular to the time y-4=-2(x+3)

Perpendicular lines have a slope that is equal to the negative inverse.
Slope is m=-2 so the new slope would be m=-(-1/2)=+1/2

Then use point slope form y-y1=m(x-x1) to get

y-2=1/2(x-3)

y=1/2x+1/2

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boffeemadrid boffeemadrid · Answer 2 · 2021-10-29T12:22:07+02:00

The equation of line which is perpendicular to the given line and has a given point is required.

The equation of the line is [tex]y=\dfrac{1}{2}x+2[/tex].

The given line is

[tex]y-4=-2(x+3)\\\Rightarrow y-4=-2x-6\\\Rightarrow y=-2x-2[/tex]

The slope of the given line is [tex]m_1=-2[/tex]

For a line to be perpendicular we have the condition

[tex]m_1m_2=-1\\\Rightarrow m_2=\dfrac{-1}{-2}\\\Rightarrow m_2=\dfrac{1}{2}[/tex]

The point is [tex]P(2,3)[/tex]

The equation will be

[tex]y=m_2x+c\\\Rightarrow 3=\dfrac{1}{2}\times 2+c\\\Rightarrow c=3-1=2[/tex]

[tex]y=\dfrac{1}{2}x+2[/tex]

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