Question

What is the EQUATION of the line PERPENDICULAR to y=-2x+5 and passing through the point (0,2)?

Answer 1

$▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪$

The required equation is ~

$\boxed{ \sf{y = \frac{x}{2} + 2 }}$

$\large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}$

Let's find the slope of given line ~

• $y = - 2x + 5$

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 ~

• $- 2 \times n = - 1$

• $n = \dfrac{ - 1}{ - 2}$

• $n = \dfrac{1}{2}$

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 ~

• $y - y_1 = m(x - x_ 1)$

here, m = slope ~

• $y - 2 = \dfrac{1}{2} (x - 0)$

• $y - 2 = \dfrac{x}{2}$

• $y = \dfrac{x}{2} + 2$

I hope it helps ~