How do you make a perpendicular line when you're given an existing line and its equation? What's the catch?

1 Answer
Nov 15, 2015

See explanation

Explanation:

The slope #m# of a line #L# that is perpendicular to another line #L'# is the negative reciprocal of the slope #m'# of #L'#

#m = -1/m'#

Now, to determine the equation of #L#, we need any point on the line so that we can determine its #y#-intercept


Example:
Find the equation of the line #L# if it is perpendicular to the line #L'# with equation #y = 2x + 1# and #L# passes through #(1, -4)#

The slope #m'# of #L'# is 2

#=> m = -1/m' = -1/2#

Now that we have the slope, let's find the #y#-intercept.
To do this, we substitute the coordinates of a point that the line passes through. In this case, #L# passes through #(1, -4)#

#y = mx + b#

#=> -4 = -1/2(1) + b#

#=> -4 = -1/2 + b#

#=> b = -4 + 1/2#

#=> b = -7/2#

Hence, the equation of the line #L# is

#y = -1/2x - 7/2#