Answer:
slope of perpendicular line - m = -1/2
passing through (-2,3)
thus,
y-3 = -1/2 (x+2)
or y = -1/2x +2
An equation of the straight line perpendicular to [tex]\boldsymbol{y=2x-5}[/tex] which passes through [tex]\boldsymbol{(-2,3)}[/tex] is [tex]\boldsymbol{x+2y-4=0}[/tex]
An equation of a straight line is [tex]\boldsymbol{y=2x-5}[/tex]
Compare this equation with the form [tex]\boldsymbol{y=mx+b}[/tex] where [tex]\boldsymbol{m,b}[/tex] denote slope and [tex]\boldsymbol{y-}[/tex]intercept respectively.
So,
[tex]\boldsymbol{m=2}[/tex]
As the slopes of two perpendicular lines are negative reciprocals of each other, slope of a required line is equal to [tex]n=\frac{-1}{2}[/tex]
Take [tex](x_1,y_1)=(-2,3)[/tex]
Equation of the required line is [tex]\boldsymbol{y-y_1=n(x-x_1)}[/tex]
[tex]y-3=\frac{-1}{2}(x+2)[/tex]
[tex]2y-6=-1(x+2)[/tex]
[tex]x+2y-4=0[/tex]
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