[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 ~
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 ~
