Which line is perpendicular to 2x-8y plus 23 equals 0?

Answer 1

4x + y + c = 0

or, for a line going through a given point (xo, yo):

y + 4x - (xo + yo) = 0

The gradient of a line multiplied by the gradient of a line perpendicular to it is -1; or in other words:

The gradient of the perpendicular line is the negative reciprocal of the gradient of the line.

Thus:

2x - 8y + 23 = 0

⇒ 8y = 2x + 23

⇒ y = 1/4x + 23/8

⇒ gradient of perpendicular line is -1 ÷ 1/4 = -4

Thus the equation of the perpendicular line to 2x - 8y + 23 = 0 is 4x + y + c = 0.

To find the line through point (xo, yo) perpendicular to 2x - 8y + 23 = 0, use the format:

y - yo = m(x - xo)

⇒ y - yo = -4(x - xo)

⇒ y + 4x - (xo + yo) = 0