What is the equation of the line that is perpendicular to 2x + 4y = 1 and that passes through the point (6, 8)?

1 Answer
Dec 12, 2016

Answer:

#y = 2x - 4#

Explanation:

Step 1) Solve for #y# in order to find the slope of the line in the equation given:

#2x + 4y = 1#

#2x - 2x + 4y = 1 - 2x#

#0 + 4y = -2x + 1#

#4y = -2x + 1#

#(4y)/4 = (-2x)/4 + 1/4#

#y = -1/2x + 1/4#

Therefore the slope is #-1/2# and the slope of the perpendicular line is the flipped and negative of this: #- -2/1 -> +2 -> 2#

Step 2) Use the point slope for to obtain the equation for the perpendicular line:

#y - 8 = 2(x - 6)#

#y - 8 = 2x - 12#

#y - 8 + 8 = 2x - 12 + 8#

#y - 0 = 2x - 4#

#y = 2x - 4#