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