y   =  - 2x  -  4

m1 = -2

m2   = 1/2

y  +  8   = (1/2)  ( x  - 2 )

y   = (1/2) x  -  9

If you put the equation of the given line into

slope, y-intercept form, you get y = -2x -4, where

(-2) is the slope. Any perpendicular line will have

slope = (1/2). Let L be such a line whose equation is in slope, y-intercept form, ie., y = mx +b, where m is the slope and b is the y-intercept

Now L has slope = (1/2) and passes through

P(1,-8). So we have L: y=(1/2)x + b...(1). We put

the x and y values of P in (1) & solve for b.

-8 = (1/2)(1) +b, ie., b = -8-(1/2) = -17/2. Then

we have L: y = (1/2)x- (1/2)17...(2). Prefer the

standard form of equation getting rid of the

fractions? Transpose y to the right side of (2) &

multiply through by 2 getting x-2y-17 = 0.

2x+y = -4 ⇒ y = -2x - 4 has a slope of -2,

so perpendicular line will have a slope of ½.

The equation of the perpendicular line passing through (2,-8) is

(y - -8) = ½(x - 2)

y = ½ x - 9....................ANS (see graph below)

2x + y = - 4

y = - 2x - 4

m2 = - 1/m

m2 = - 1/(-2)

m2 = 1/2

y - y1 = m(x - x1)

y - (-8) = 1/2(x - 2)

2(y + 8) =x - 2

 2y + 16 = x - 2

 2y = x - 2 - 16

2y = x - 18

y = 1/2x - 9 answer//   

therefore, the equation of the line is y = 1/2x - 9 ..//

Perpendicular slope: 1/2 or 0.5

Point; (2, -8)Perpendicular equation: y = 0.5x -9

At first glance 2x+y=−4 and passes through the point (2, −8), so the equation is 2x+y=−4.

However, the line perpendicular to ax+by=c through a given point (x₀,y₀) is bx-ay=bx₀-ay₀. Here this is 2x + y = 2×2 + -8 which simplifies to 2x + y = -4.

Slope of (2x + y = -4) = -2/1 = -2

Slope of the required line = -1/(-2) = 1/2

Equation of the required line:

y - (-8) = (1/2)(x - 2)

2(y + 8) = x - 2

2y + 16 = x - 2

x - 2y - 18 = 0