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[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

The required equation is ~

[tex] \boxed{ \sf{y = \frac{x}{2} + 2 }}[/tex]

[tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]

Let's find the slope of given line ~

  • [tex]y = - 2x + 5[/tex]

comparing it with general slope - intercept form of line (y = mx + c) we get, m = -2 (that is slope of the line)

let the slope of the required line be n

And, now since the required line Is perpendicular to the given line. the product of their slopes is -1

that is ~

  • [tex] - 2 \times n = - 1[/tex]

  • [tex]n = \dfrac{ - 1}{ - 2} [/tex]

  • [tex]n = \dfrac{1}{2} [/tex]

slope of required line is ~ 1/2

now, let's use the point - slope form of line to find the equation of required (perpendicular) line (using point (0 , 2) ~

that is ~

  • [tex]y - y_1 = m(x - x_ 1)[/tex]

here, m = slope ~

  • [tex] y - 2 = \dfrac{1}{2} (x - 0)[/tex]

  • [tex]y - 2 = \dfrac{x}{2} [/tex]

  • [tex]y = \dfrac{x}{2} + 2[/tex]

I hope it helps ~

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